1MA 05. RECTES EN EL PLA/1MA.05.2 //// i ┴ 1MA.05.2.10DT PARAL·LELISME: VECTORS  
Paral·lelisme: vectors
2 rectes són paral·leles si, i només si, els seus vectors directors són dependents (proporcionals):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

 

 
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 0.0000000 0.0000000 0 1MA.05.2.11Q //?(vectors) ParamCont Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>e11</mi><mo>,</mo><mi>e12</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n1</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» per esbrinar si són proporcionals

 

]]> 1MA.05.2.12Q //?(vectors) CartCont Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>11</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» perquè amb ax+by+c=0 un vector director és (-b,a)

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» per esbrinar si són proporcionals

 

]]> 1MA.05.2.13Q //?(vectors) ExplCont Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></mrow><mi>u1</mi></mfrac><mo>+</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mn>3</mn></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» perquè en l'equació explícita y=mx+n, un vector director és [1,m]

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math» perquè, en l'equació contínua, els components d'un vector director són els denominadors.

Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» per esbrinar si són proporcionals

 

]]> 1MA.05.2.15Q Determinar m per r i s paral·leles Per a quin valor de m  les rectes r i s són paral·leles?
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»
s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mstyle»«/math»

Format de la resposta: -2/3: enter o fracció simplificada


]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>b2</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>v1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>m</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>v1</mi><mo>*</mo><mi>u2</mi></mrow><mi>u1</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»[«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mstyle»«/math».

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«/mstyle»«/math».

Per tal que siguin paral·leles, cal que els vectors siguin proporcionals i que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.20 DT PARAL·LELISME I PENDENT  
Paral·lelisme: pendents

2 rectes són paral·leles si, i només si, els seus pendents són iguals.

 

 
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0.0000000 0.0000000 0 1MA.05.2.21Q //?(pendent) ParamCont (còpia) Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»


a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>e11</mi><mo>,</mo><mi>e12</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n1</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

Compara'ls 

 

]]> 1MA.05.2.22Q //?(pendent) CartCont Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mn>1</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«/mstyle»«/math» perquè amb ax+by+c=0 un vector director és (-b,a)

Un vector de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«/mstyle»«/math» ja que, en l'equació contínua, els components són els denominadors.

Calcula els pendents i compara.

 

]]> 1MA.05.2.23Q //?(pendent) ContExplícita Considera les rectes d'equacions:
 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
 
a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format:  S si ho són i N si no ho són.

 

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Paral</mi><mo>·</mo><mi>leles</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></mrow><mi>u1</mi></mfrac><mo>+</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>37</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«/mstyle»«/math» perquè, en l'equació contínua, el vector ve determinat pels denominadors

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«/mstyle»«/math» perquè, en l'equació explícita y =mx+n, el vector és [1,m]

Calcula  els pendents i compara'ls

 

]]> 1MA.05.2.30DT TROBAR RECTA //  
Escriure l'equació d'una recta paral·lela

AMB VECTORS

Per escriure l'equació de la recta s, paral·lela a la recta r,  fem servir el punt per on passa s i un vector director de r.

Exemple: Si r és 2x-3y+5=0 té, (3,2) també és vector director de s. Si s passa pel punt (2,-2) la seva equació contínua és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨normal¨»y«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» d'on es poden deduir les altres equacions.

AMB PENDENTS

Una recta paral·lela a la recta r té el mateix pendent que r.

Exemple: Una recta paral·lela a r: =2x-1 té per pendent 2 i s'escriu y = 2x + n.

Si passa pel punt (2,-2), substituint x i y es troba que -2 = 2·2 + n,   o sigui  n = -6.

L'equació explícita és doncs y = 2x-6

 

 
]]> 0.0000000 0.0000000 0 1MA.05.2.31Q EqContinuaDe // cartesiana Troba l'equació contínua d'una recta s que és paral·lela a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»i que passa per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math».
#G1


]]> L'equació és  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

i les rectes són #G2

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>e1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>n2</mi><mo>,</mo><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn><mo>,</mo><mi>y</mi><mo>+</mo><mn>9</mn><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>9</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math».

Com que s és paral·lela a r, aquest vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» també és director de s.

Per escriure l'equació contínua de s, ja tenim:

  • un punt A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«/mrow»«/mstyle»«/math»  → als numeradors
  • i un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» → als denominadors
]]> 1MA.05.2.32Q EqCartesianaDe // paramètriques Troba l'equació cartesiana d'una recta s que és paral·lela a la recta r d'equacions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i que passa per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math».
#G1


]]> El gràfic és: #G2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>u</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>∉</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>r1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>r2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u11</mi><mo>=</mo><mo>-</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mo>(</mo><mi>u2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>-</mo><mi>u11</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi><mo>+</mo><mi>u1</mi><mo>*</mo><mi>a2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi><mo>+</mo><mi>u1</mi><mo>*</mo><mi>a2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>m</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>m</mi><mi>u2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>6</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>k</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>16</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>,</mo><mi>G2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi><mo>,</mo><mi>tauler2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m1</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>y</mi><mo>-</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que són paral·leles, el vector director de r, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math», és director de s.

  • Mètode 1: escrius l'equació contínua amb el punt A i el vector de r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i la transformes a cartesiana

 

  • Mètode 2: l'equació cartesiana d'una recta que té per vector director «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math». Per trobar el valor de c, només cal pensar que la recta passa per A, i substituir x i y per les coordenades de A.

 

 

]]>
  •  Mètode 1: Es treuen denominadors amb el mcm dels denominadors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«/mstyle»«/math»: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math» i es transposen tots els termes a l'esquerra per igualar a zero

    •  

    • Mètode 2: L'equació és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math». Calcula c substituint x i y per les coordenades de A: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»
    ]]>         1MA.05.2.33Q EqExplícitaDe // explícita Troba l'equació explícita d'una recta s que passa per A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i que és paral·lela a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math».

    #G1

    ]]>         Gràficament: #G2

    ]]>         1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a2</mi><mo>≠</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>+</mo><mi>n</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que són paral·leles, tenen el mateix pendent, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«/mstyle»«/math»,  i l'equació de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«/mrow»«/mstyle»«/math».

    Per a trobar n, cal substituir x i y per les coordenades del punt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«/mrow»«/mstyle»«/math»

    ]]>         1MA.05.2.40DT PERPENDICULARITAT(VECTORS)

    Condició de perpendicularitat amb vectors
     
    2 rectes són perpendiculars si, i només si, els seus vectors directors són perpendiculars, o sigui si el seu producte escalar és 0:
    x1·x2 + y1·y2 = 0
     

     

    ]]>         0.0000000 0.0000000 0     1MA.05.2.41Q ┴ vectorsContCont Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    a) Calcula el producte escalar dels seus vectors directors

    b) Esbrina si són perpendiculars: S per si, N per no.

    ]]>         Gràfic (r en blau, s en verd)

    #G1

    ]]>         1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u1</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>u2</mi><mo>*</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>u2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n3</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n4</mi><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>a</mi><mi>r</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

    Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

    El producte escalar és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

    ]]>         1MA.05.2.42Q ┴ vectorsContCart Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    a) Calcula el producte escalar dels seus vectors directors

    b) Esbrina si són perpendiculars: S per si, N per no.

    ]]>         Gràfic (r en blau, s en verd)

    #G1

    ]]>         1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u1</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>u2</mi><mo>*</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>u2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>6</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>a</mi><mi>r</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

    Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

    El producte escalar és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

    ]]>         1MA.05.2.43Q ┴ vectorsParamCart Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    a) Calcula el producte escalar dels seus vectors directors

    b) Esbrina si són perpendiculars: S per si, N per no.

    ]]>         Gràfic (r en blau, s en verd)

    #G1

    ]]>         1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u1</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>u2</mi><mo>*</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math 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align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>6</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>6</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>&#xA0;</mo><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>a</mi><mi>r</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

    Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

    El producte escalar és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

    ]]>         1MA.05.2.50DT PERPENDICULARITAT(PENDENTS)

    Perpendicularitat amb pendents
     
    2 rectes són perpendiculars si, i només si, els seus pendents m i m' són tal que:
     
    m · m' = -1

     

    ]]>         0.0000000 0.0000000 0     1MA.05.2.51Q ┴ pendentContCart Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    a) Calcula el producte dels seus pendents

    b) Esbrina si són perpendiculars: S per si, N per no.

    ]]>         Gràfic (r en blau, s en verd)

    #G1

    ]]>         1.0000000 0.5000000 0 0 a. Producte=#sol1b. Perpendiculars?(S/N) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math 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open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>u2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable 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align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>y</mi><mo>+</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El pendent  de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

    El pendent  de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

    Multiplica'ls

    ]]>         1MA.05.2.52Q ┴ pendentExplícitaCartesiana Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    a) Calcula el producte dels seus pendents

    b) Esbrina si són perpendiculars: S per si, N per no.

    ]]>         Gràfic (r en blau, s en verd)

    #G1

    ]]>         1.0000000 0.5000000 0 0 a. Producte=#sol1b. Perpendiculars?(S/N) =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>,</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo>&#xA0;</mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El pendent  de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

    El pendent  de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

    Multiplica'ls

    ]]>         1MA.05.2.55Q Tobar m per ┴ (vec/pend) Considera les rectes d'equacions:
    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

    Per quin valor de m són perpendiculars?

    ]]>         1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo>&nbsp;</mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>m</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v1</mi></mrow><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math 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type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
  • Resolució amb els vectors directors

    • Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

    Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

    Cal que  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mstyle»«/math»= 0

    • Resolució amb els pendents

    El pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

    El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

    Cal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

    ]]>         1MA.05.2.60DT EQ RECTA PERPENDICULAR  
    Escriure l'equació d'una recta perpendicular

    AMB VECTORS

    Per escriure l'equació de la recta perpendicular a la recta r de vector director (A,B)  fem servir un punt i el vector (-B,A) que és perpendicular a (A,B)

    Exemple: Una perpendicular a r : 2x-3y+5=0 té per vector director (-2,3). Si passa pel punt (2,-2) la seva equació contínua és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mn»3«/mn»«/mfrac»«/mrow»«/mstyle»«/math» d'on es poden deduir les altres equacions.

    AMB PENDENTS

    Una recta perpendicular a la recta r (de pendent m) té un pendent m' tal que:

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

    Exemple: Una recta perpendicular a r: =2x-1 té per pendent -1/2 i s'escriu y = -1/2·x + n.

    Si passa pel punt (2,-2), substituint x i y es troba que -2 = -1/2·2 + n,   o sigui  n = -1.

    L'equació explícita és doncs y = -1/2·x-1

     

     
    ]]>         0.0000000 0.0000000 0     1MA.05.2.61Q EqContinua ┴ cartesiana Troba l'equació contínua d'una recta s que és perpendicular a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» i que passa per A «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«/mstyle»«/math».
    #G1


    ]]>         Resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

    #G2

    ]]>         1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math».

    Un vector perpendicular a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math»

    Per escriure l'equació contínua de s, ja tenim:

    • un punt A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math»  → als numeradors
    • i un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» → als denominadors
    ]]>         1MA.05.2.62Q EqExplícita ┴ explícita Troba l'equació explícita de la recta s que passa per A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i que és perpendicular a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math».
    #G1
    ]]>         #G2

    ]]>         1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>v1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a2</mi><mo>≠</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>+</mo><mi>n</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mi>m</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>a2</mi><mo>+</mo><mfrac><mi>a1</mi><mi>m</mi></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math 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align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per l'equació explicita y = mx + n

    • Mètode ràpid: determinar m i n amb les dades del problema.

    Com que són perpendiculars, si m`és el pendent de r, el pendent m de s és tal que m·m'=-1:  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

    L'equació de s s'escriu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«/mrow»«/mstyle»«/math»

    Per calcular  n, cal substituir x i y per les coordenades del punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»:

    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«/mrow»«/mstyle»«/math»

     

    • Mètode interminable: fent servir vectors i el producte escalar

    Determinar el vector director de r, fent nul el producte escalar i a partir de l'equació contínua, amb el punt i el vector, arribar fins l'equació explícita.

    ]]>