1MA 04. VECTORS/1MA.04.5 Problemes amb vectors 1MA.04.5.21Q VectorUnitariDependent Determina els components d’un vector unitari sabent que és perpendicular al vector (#a1,#a2).

Es recorda que el mòdul d'un vector unitari és 1.

Format de la resposta: [2,3] Simplificat

]]> 1.0000000 0.5000000 0 0 #sol2 #sol3 <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mfrac><mi>a1</mi><mi>a2</mi></mfrac><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt><mn>7</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>85</mn></msqrt><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mrow><mn>7</mn><mo>*</mo><mi>x</mi></mrow><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mfrac><mo>,</mo><mfrac><mrow><mn>6</mn><mo>*</mo><mi>x</mi></mrow><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mn>7</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac><mo>,</mo><mfrac><mrow><mn>6</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>7</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>6</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>,</mo><mi>a6</mi><mo>,</mo><mi>a7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>36</mn><mn>49</mn></mfrac><mo>,</mo><mfrac><mn>85</mn><mn>49</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>85</mn></msqrt><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol2</correctAnswer><correctAnswer id="1">#sol3</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></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> Sigui (x,y) el vector perpendicular.

El producte escalar ha de ser nul:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»x«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»el«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»vector«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»`«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»escriu«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

]]> Ara cal que el mòdul del vector, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«/mstyle»«/math» , sigui 1.

Dividim pel mòdul: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#000066¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«msqrt mathcolor=¨#000066¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«msqrt mathcolor=¨#000066¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«/mstyle»«/math»

El vector demanat és doncs:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mfrac»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»,«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»,«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

i es racionalitza, si cal!

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