Álgebra/Tema 8: Vectores (operatoria)/Revisar JG_A1_28 Vectores - F Determine las coordenadas del punto medio entre los siguientes vectores:

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

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Nota: Escriba el resultado de la misma forma en que se muestran los vectores anteriores.

]]> 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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mi>a1</mi><mo>+</mo><mi>b1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a3</mi><mo>+</mo><mi>b3</mi></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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_28 Vectores: punto medio con parametro - F Determine las coordenadas del punto medio entre los siguientes vectores:

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

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Nota: Escriba el resultado en términos del parámetro y de la misma forma en que se muestran los vectores anteriores.

]]> 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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mi>a1</mi><mo>+</mo><mi>b1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a3</mi><mo>+</mo><mi>b3</mi></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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_29 Vectores - F Si conoce el punto medio M del segmento AB y el punto A, determine B.

«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»§#160;«/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»M«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»m«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»m«/mi»«mn»3«/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>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>m1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>m2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>b</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><msqrt><mi>b</mi></msqrt><mn>4</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mn>2</mn><mo>*</mo><mi>m1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m3</mi><mo>-</mo><mi>a3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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_29 Vectores: punto dado el punto medio - F Si conoce el punto medio M del segmento AB y el punto A, determine B.

«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»§#160;«/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»M«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»m«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»m«/mi»«mn»3«/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>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>m1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>m2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>b</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><msqrt><mi>b</mi></msqrt><mn>4</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mn>2</mn><mo>*</mo><mi>m1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m3</mi><mo>-</mo><mi>a3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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_30 Vectores - F Determine la función 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»

]]> 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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>v0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>b2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mi>b3</mi><mo>-</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v0</mi><mo>+</mo><mi>t</mi><mo>*</mo><mi>v1</mi></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>6</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>*</mo><mi>t</mi><mo>-</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>15</mn><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_31 Vectores - D Encuentre la ecuación del plano que contiene a la recta:

«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» 

]]> 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>x01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>y01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>z01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>x12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>y12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>z12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>x12</mi><mo>*</mo><mi>x</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>y12</mi><mo>*</mo><mi>y</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>z12</mi><mo>*</mo><mi>z</mi><mo>&nbsp;</mo><mo>-</mo><mo>(</mo><mi>x12</mi><mo>*</mo><mi>x01</mi><mo>+</mo><mi>y12</mi><mo>*</mo><mi>y01</mi><mo>+</mo><mi>z12</mi><mo>*</mo><mi>z01</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"><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>+</mo><mn>74</mn></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_32 Distancia - M Determine la mínima distancia al punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» entre los siguientes planos:

«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»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/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»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/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»2«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>x1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>p0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dis1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>x2</mi><mo>+</mo><mi>c1</mi><mo>*</mo><mi>x3</mi><mo>-</mo><mi>d1</mi></mrow></mfenced><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c1</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dis2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a2</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>b2</mi><mo>*</mo><mi>x2</mi><mo>+</mo><mi>c2</mi><mo>*</mo><mi>x3</mi><mo>-</mo><mi>d2</mi></mrow></mfenced><msqrt><mrow><msup><mi>a2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c2</mi><mn>2</mn></msup></mrow></msqrt></mfrac></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>dis1</mi><mo>&nbsp;</mo><mo>&gt;</mo><mo>&nbsp;</mo><mi>dis2</mi></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>dis2</mi></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>dis1</mi></mrow></apply></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_33 Triángulo - M Determine el área de un triángulo dados los siguientes puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»3«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»3«/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>v11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><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>v21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><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>v32</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v33</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v11</mi><mo>,</mo><mi>v12</mi><mo>,</mo><mi>v13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v21</mi><mo>,</mo><mi>v22</mi><mo>,</mo><mi>v23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v31</mi><mo>,</mo><mi>v32</mi><mo>,</mo><mi>v33</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v2</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v3</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>V21</mi><mo>×</mo><mi>V31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="‖" open="‖"><mi>w</mi></mfenced><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</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><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>,</mo><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><mn>23</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><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"><mfrac><msqrt><mrow><mn>9</mn><mo>*</mo><msup><mi>a</mi><mn>4</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>-</mo><mn>604</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>3520</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>50816</mn></mrow></msqrt><mn>16</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>#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_33 Vectores - M Determine el área de un triángulo dados los siguientes vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»3«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»3«/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>v11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><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>v21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><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>v32</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v33</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v11</mi><mo>,</mo><mi>v12</mi><mo>,</mo><mi>v13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v21</mi><mo>,</mo><mi>v22</mi><mo>,</mo><mi>v23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v31</mi><mo>,</mo><mi>v32</mi><mo>,</mo><mi>v33</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v2</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v3</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>V21</mi><mo>×</mo><mi>V31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="‖" open="‖"><mi>w</mi></mfenced><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</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><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>,</mo><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><mn>23</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><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"><mfrac><msqrt><mrow><mn>9</mn><mo>*</mo><msup><mi>a</mi><mn>4</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>-</mo><mn>604</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>3520</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>50816</mn></mrow></msqrt><mn>16</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>#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_34 Ángulo Planos - M Encuentre el ángulo formado entre los planos:

«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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mo>&nbsp;</mo><mi>b1</mi><mo>,</mo><mo>&nbsp;</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a2</mi><mo>,</mo><mo>&nbsp;</mo><mi>b2</mi><mo>,</mo><mo>&nbsp;</mo><mi>c2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>*</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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».

 

]]> 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>A0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>A1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>B1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>C0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>C1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>B0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>B1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>C0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>C1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>V1</mi><mo>*</mo><mi>V2</mi></mrow><mfenced close="‖" open="‖"><mi>V2</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>11</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"><mfrac><mrow><mn>42</mn><mo>*</mo><msqrt><mn>137</mn></msqrt></mrow><mn>137</mn></mfrac></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^(-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_36 Producto Punto - F Si conoce los vectores:

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

Calcule las siguientes expresiones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mn»2«/mn»«mo»§#183;«/mo»«mi»B«/mi»«mo»§#183;«/mo»«mi»C«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»C«/mi»«mo»§#183;«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«/mfenced»«/math»: {#3}

]]> 3.0000000 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>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>c3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</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>A</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</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>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mn>2</mn><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>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>A</mi><mo>*</mo><mi>B</mi><mo>*</mo><mi>C</mi></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"><mn>26</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"><mn>206</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>182</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><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^(-1)</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>