Álgebra/Tema 9: Rectas y Planos ER_A1_00_D - 191114 - Región Geométrica ER_A1_00

Considere el conjunto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced»«mrow»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»,«/mo»«mi»z«/mi»«/mrow»«/mfenced»«mo»§#8712;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo»:«/mo»«mo»#«/mo»«mi»E«/mi»«mi»C«/mi»«/mrow»«/mfenced»«/math»

Determine a que región geométrica corresponde el conjunto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" 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"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><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"><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><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"><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><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"><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><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>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></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"/></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>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>plano</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>"</mo><mi>Una</mi><mo> </mo><mi>recta</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>punto</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>"</mo><mi>Vacío</mi><mo>"</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>plano</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>"</mo><mi>Una</mi><mo> </mo><mi>recta</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>punto</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>"</mo><mi>Vacío</mi><mo>"</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>f</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>e</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>e</mi><mo>≠</mo><mi>f</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>plano</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>"</mo><mi>Una</mi><mo> </mo><mi>recta</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>punto</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>"</mo><mi>Vacío</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo> </mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo> </mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>plano</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>"</mo><mi>Una</mi><mo> </mo><mi>recta</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>"</mo><mi>Un</mi><mo> </mo><mi>punto</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>"</mo><mi>Vacío</mi><mo>"</mo></mtd></mtr></mtable><mn>5</mn></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</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>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</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>c</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>EC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>9</mn></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"><ms>Un</ms><mo> </mo><ms>plano</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>L</mi><mo>,</mo><mn>3</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><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="casSession"/></localData></question> JG_A1_30 Vectores: ecuacion vectorial de la recta - F Determine la ecuación vectorial de la recta que pasa a través de los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Escribir resultado de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«mo»+«/mo»«mi»t«/mi»«mo»§#183;«/mo»«mo»[«/mo»«mi»x«/mi»«mn»1«/mn»«mo»,«/mo»«mi»y«/mi»«mn»1«/mn»«mo»,«/mo»«mi»z«/mi»«mn»1«/mn»«mo»]«/mo»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»01«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«mn»7«/mn»«/mfrac»«mo»=«/mo»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»y«/mi»«mn»01«/mn»«mo»=«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»z«/mi»«mn»01«/mn»«/math»

Y es perpendicular a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»7«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»17«/mn»«mo»+«/mo»«mo»#«/mo»«mi»z«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«/math»

Con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#960;«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»§#960;«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Responder de la siguiente forma, por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»{«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5631«/mn»«mo»}«/mo»«mo»}«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>a1</mi><mo>,</mo><mo> </mo><mi>b1</mi><mo>,</mo><mo> </mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>a2</mi><mo>,</mo><mo> </mo><mi>b2</mi><mo>,</mo><mo> </mo><mi>c2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo> </mo><mo>=</mo><mo> </mo><mi>n1</mi><mo> </mo><mo>*</mo><mo> </mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N1</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mi>n1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N2</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>nn</mi><mrow><mi>N1</mi><mo>*</mo><mi>N2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>resolver</mi><mfenced><mrow><mi>cos</mi><mo>(</mo><mi>ang</mi><mo>)</mo><mo>=</mo><mi>x</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</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>1</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</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>2</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0.94958</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</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> JG_A1_35 Proyección - F Dados los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»A«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»A«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»B«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»C«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»C«/mi»«mn»1«/mn»«mo»)«/mo»«/math»

Calcule la proyección del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«/munder»«/math» sobre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»C«/mi»«/mrow»«/munder»«/math».

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»y«/mi»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mfrac»«mi»z«/mi»«mn»1«/mn»«/mfrac»«/math»

con el plano:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»-«/mo»«mn»6«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»

Expresado en forma vectorial, como por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Encontrar la ecuación del plano que pasa por el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»v«/mi»«/math» y es perpendicular a la intersección de los planos dados.

Responder de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mi»d«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>x0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>,</mo><mi>z0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d0</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>a0</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b0</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>zz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>a0</mi><mo>,</mo><mi>b0</mi><mo>,</mo><mi>c0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mi>n1</mi><mo>×</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x</mi><mo>-</mo><mi>x0</mi><mo>,</mo><mi>y</mi><mo>-</mo><mi>y0</mi><mo>,</mo><mi>z</mi><mo>-</mo><mi>z0</mi><mo>]</mo><mo>*</mo><mi>n</mi></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_39 Distancia Recta-Punto - M Hallar la distancia desde el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» a la recta que une los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>p01</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p02</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p03</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p13</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p23</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p01</mi><mo>,</mo><mo> </mo><mi>p02</mi><mo>,</mo><mo> </mo><mi>p03</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p11</mi><mo>,</mo><mo> </mo><mi>p12</mi><mo>,</mo><mo> </mo><mi>p13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p21</mi><mo>,</mo><mo> </mo><mi>p22</mi><mo>,</mo><mo> </mo><mi>p23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo> </mo><mo>=</mo><mo> </mo><mi>p2</mi><mo> </mo><mo>-</mo><mo> </mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mi>m</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>m</mi><mi>mm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo> </mo><mo>=</mo><mo> </mo><mi>p0</mi><mo> </mo><mo>-</mo><mo> </mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mrow><mi>p</mi><mo>×</mo><mi>mu</mi></mrow></mfenced></math></input></command></group></library><group><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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>13</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>221</mn></msqrt></mrow><mn>13</mn></mfrac></math></output></command></group><group><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>#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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_39 Distancia Recta-Punto - M Hallar la distancia desde el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» a la recta que une los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>p01</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p02</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p03</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p13</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p23</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p01</mi><mo>,</mo><mo> </mo><mi>p02</mi><mo>,</mo><mo> </mo><mi>p03</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p11</mi><mo>,</mo><mo> </mo><mi>p12</mi><mo>,</mo><mo> </mo><mi>p13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>p21</mi><mo>,</mo><mo> </mo><mi>p22</mi><mo>,</mo><mo> </mo><mi>p23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo> </mo><mo>=</mo><mo> </mo><mi>p2</mi><mo> </mo><mo>-</mo><mo> </mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mi>m</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mi>m</mi><mi>mm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo> </mo><mo>=</mo><mo> </mo><mi>p0</mi><mo> </mo><mo>-</mo><mo> </mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mfenced close="‖" open="‖"><mrow><mi>p</mi><mo>×</mo><mi>mu</mi></mrow></mfenced></math></input></command></group></library><group><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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>13</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>221</mn></msqrt></mrow><mn>13</mn></mfrac></math></output></command></group><group><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>#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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_40 Vector Normal Plano - M A partir de los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»

Encuentre el vector normal del plano que se forma.

Responder de la siguiente manera:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>x1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>{</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo> </mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo> </mo><mfrac><msqrt><mi>a</mi></msqrt><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y3</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z3</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>z1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>z3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><mi>p2</mi><mo>-</mo><mi>p1</mi><mo>)</mo><mo>×</mo><mo>(</mo><mi>p3</mi><mo>-</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><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"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mfrac><mrow><mn>9</mn><mo>*</mo><msqrt><mi>a</mi></msqrt></mrow><mn>2</mn></mfrac><mo>+</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>*</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_41 Proyección - D Sea la recta L que une los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

Encuentre la ecuación de la proyección de la recta L, sobre el plano «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»

Responda de la forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»§#955;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mi»Q«/mi»«mo»-«/mo»«mi»P«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>x1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>z1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo> </mo><mo>=</mo><mo> </mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>(</mo><mi>d</mi><mo> </mo><mo>-</mo><mo> </mo><mi>x2</mi><mo> </mo><mo>-</mo><mo> </mo><mi>y2</mi><mo> </mo><mo>-</mo><mo> </mo><mi>z2</mi><mo>)</mo></mrow><mrow><mi>x1</mi><mo>+</mo><mi>y1</mi><mo>+</mo><mi>z1</mi><mo>-</mo><mi>x2</mi><mo>-</mo><mi>y2</mi><mo>-</mo><mi>z2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>x2</mi><mo>,</mo><mo> </mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>y2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>y2</mi><mo>,</mo><mo> </mo><mo>(</mo><mi>z1</mi><mo>-</mo><mi>z2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xq</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yq</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>y2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zq</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>z2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>(</mo><mi>x2</mi><mo>+</mo><mi>y2</mi><mo>+</mo><mi>z2</mi><mo>+</mo><mi>d</mi><mo>)</mo></mrow><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo> </mo><mo>=</mo><mo> </mo><mo>[</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>x2</mi><mo>,</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>y2</mi><mo>,</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo> </mo><mo>=</mo><mo> </mo><mi>P</mi><mo> </mo><mo>+</mo><mi>λ</mi><mo>*</mo><mo>(</mo><mi>Q</mi><mo>-</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_33 Vectores Perpendiculares Determine cuál(es) de los siguientes vectores es(son) perpendicular(es) al vector:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

NOTA: Puede existir más de alguno

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> ( #a , #c , -#b)

]]> ( -#b , -#a , 0)

]]> (-#c , -#c , #k)

]]> (-#c , 0 , #a)

]]> (-#a , -#b , -#c)

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>=</mo><mi>bb</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>cc</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mfenced close="‖" open="‖"><mi>ab</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>ac</mi></mfenced></math></input></command></group></library><group><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"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</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>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><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>ac</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>16</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"><mn>5</mn><mo>*</mo><msqrt><mn>178</mn></msqrt></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_35 Volumen Paralelepípedo Calcular el volumen del paralelepípedo que tiene un vértice en el origen y los lados definidos por los VECTORES

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aaa</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bbb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>bbb</mi><mo>×</mo><mi>ccc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>m</mi><mo>=</mo><mo>=</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></mrow><mtable><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>bbb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>ccc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>bbb</mi><mo>×</mo><mi>ccc</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>aaa</mi><mo>*</mo><mi>m</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aaa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>8</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>8</mn></mrow></mfenced></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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>28</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>28</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bbb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>8</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</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"><mn>84</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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_36 Ecuación paramétrica Determine la ecuación paramétrica de la recta que contiene a los puntos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»Q«/mi»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

Complete:

x = {#1} + t {#2}

y = {#3} + t {#4} ; "t" pertenece a los reales

z = {#5} + t {#6}

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" 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>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tx</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ty</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tz</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><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="casSession"/></localData></question> VA_AI_36 Ecuación paramétrica Determine la ecuación paramétrica de la recta que contiene a los puntos

Complete:

x = {#1} + t {#2}

y = {#3} + t {#4} ; "t" pertenece a los reales

z = {#5} + t {#6}

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" 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>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tx</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ty</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tz</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><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="casSession"/></localData></question> VA_AI_37 Vector director Determine el vector director de la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#160;«/mo»«mi»z«/mi»«/math»

Nota: Escriba el vector como una matriz de 1 Fila y 3 Columnas

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

y que es paralela a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»;«/mo»«mo»§#160;«/mo»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

Nota: Escriba el punto y el vector director como matrices de 1 fila y 3 columnas.

Nota 2: Use " t " como el parámetro.

(x,y,z) =