Tema 9: Rectas y Planos 015 ecuación paramétrica de la recta Dados los puntos #A1 y #A2, determine la ecuación paramétrica en términos del parámetro «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«/math» que la define:

]]> 1.0000000 0.3333333 0 0 x=#x1y=#y1z=#z1]]> <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>z1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced close="|" open="|"><mi>k1</mi></mfenced><mo>+</mo><mfenced close="|" open="|"><mi>k2</mi></mfenced><mo>≠</mo><mn>0</mn><mo>∧</mo><mfenced close="|" open="|"><mi>d1</mi></mfenced><mo>+</mo><mfenced close="|" open="|"><mi>d2</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>k1</mi><mo>*</mo><mi>z1</mi><mo>+</mo><mi>d1</mi><mo>,</mo><mi>k2</mi><mo>*</mo><mi>z1</mi><mo>+</mo><mi>d2</mi><mo>,</mo><mi>z1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>k1</mi><mo>*</mo><mi>z2</mi><mo>+</mo><mi>d1</mi><mo>,</mo><mi>k2</mi><mo>*</mo><mi>z2</mi><mo>+</mo><mi>d2</mi><mo>,</mo><mi>z2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>A1</mi><mn>1</mn></msub><mo>+</mo><mi>t</mi><mo>*</mo><mo>(</mo><msub><mi>A2</mi><mn>1</mn></msub><mo>-</mo><msub><mi>A1</mi><mn>1</mn></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msub><mi>A1</mi><mn>2</mn></msub><mo>+</mo><mi>t</mi><mo>*</mo><mo>(</mo><msub><mi>A2</mi><mn>2</mn></msub><mo>-</mo><msub><mi>A1</mi><mn>2</mn></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><msub><mi>A1</mi><mn>3</mn></msub><mo>+</mo><mi>t</mi><mo>*</mo><mo>(</mo><msub><mi>A2</mi><mn>3</mn></msub><mo>-</mo><msub><mi>A1</mi><mn>3</mn></msub><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>k1</mi><mo>*</mo><mi>z</mi><mo>-</mo><mi>d1</mi><mo>=</mo><mn>0</mn><mo>∧</mo><mi>y</mi><mo>-</mo><mi>k2</mi><mo>*</mo><mi>z</mi><mo>-</mo><mi>d2</mi><mo>=</mo><mn>0</mn><mo>∧</mo><mfenced><mrow><apply><diff/><bvar><mi>t</mi></bvar><mi>x</mi></apply><mo>≠</mo><mn>0</mn><mo>∨</mo><apply><diff/><bvar><mi>t</mi></bvar><mi>y</mi></apply><mo>≠</mo><mn>0</mn><mo>∨</mo><apply><diff/><bvar><mi>t</mi></bvar><mi>z</mi></apply><mo>≠</mo><mn>0</mn></mrow></mfenced><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A1</mi><mn>1</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>z1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 016 Distancia entre puntos 2D, infinitas respuestas Determine las coordenadas de un punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mrow»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«/mrow»«/mfenced»«/math» del plano que esté en el #texto1 cuadrante y que está a una distancia #texto2 a #d1 unidades del punto que aparece en el plano:

#graf

]]> 1.0000000 0.3333333 0 0 a=#x1b=#y1]]> x=#x2y=#y2]]> <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"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>12</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>10</mn><mo>}</mo><mo>)</mo></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>a1</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>tercer</mi><mo>"</mo></mrow><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>segundo</mi><mo>"</mo></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>cuarto</mi><mo>"</mo></mrow><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>primer</mi><mo>"</mo></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto2</mi><mo>=</mo><mo>"</mo><mi>igual</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>máximo</mi><mo>(</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="⌉" open="⌈"><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow></msqrt></mfenced><mo>)</mo><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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>primer</mi><mo>"</mo></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>></mo><mn>0</mn><mo>∧</mo><mi>y</mi><mo>></mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>segundo</mi><mo>"</mo></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo><</mo><mn>0</mn><mo>∧</mo><mi>y</mi><mo>></mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>texto1</mi><mo>=</mo><mo>"</mo><mi>tercer</mi><mo>"</mo></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo><</mo><mn>0</mn><mo>∧</mo><mi>y</mi><mo><</mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>></mo><mn>0</mn><mo>∧</mo><mi>y</mi><mo><</mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>tercer</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>)</mo><mo>?</mo></math></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_no_more_decimals"><param name="digits">0</param></assertion><assertion name="equivalent_function"><param name="name">test</param></assertion><assertion name="syntax_expression"/><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">5</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 017 Distancia entre puntos 3D , infinitas respuestas Determine las coordenadas de un punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced»«mrow»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»,«/mo»«mi»c«/mi»«/mrow»«/mfenced»«/math» del plano que #texto1 y que está a una distancia #texto2 a #d1 unidades del punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«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»«/math» que aparece en el plano:

#graf

]]> 1.0000000 0.3333333 0 0 a=#x1b=#y1c=#z1]]> x=#x2y=#y2z=#z2]]> <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"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><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><mi>punto</mi><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>t1</mi><mo>=</mo><mi>tablero3d</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>12</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P2</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>a2</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P4</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P5</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>0</mn><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>P6</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mn>0</mn><mo>,</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P7</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>a3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P8</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mi>P4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P3</mi><mo>,</mo><mi>P4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mi>P4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mi>P6</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s5</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P3</mi><mo>,</mo><mi>P5</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s6</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mi>P5</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s7</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mi>P6</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s8</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P6</mi><mo>,</mo><mi>P7</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s9</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P5</mi><mo>,</mo><mi>P7</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s10</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P3</mi><mo>,</mo><mi>P8</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s11</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mi>P8</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s12</mi><mo>=</mo><mi>segmento</mi><mo>(</mo><mi>P7</mi><mo>,</mo><mi>P8</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi><mo>=</mo><mi>dibujar3d</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>10</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar3d</mi><mo>(</mo><mo>{</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>,</mo><mi>s3</mi><mo>,</mo><mi>s4</mi><mo>,</mo><mi>s5</mi><mo>,</mo><mi>s6</mi><mo>,</mo><mi>s7</mi><mo>,</mo><mi>s8</mi><mo>,</mo><mi>s9</mi><mo>,</mo><mi>s10</mi><mo>,</mo><mi>s11</mi><mo>,</mo><mi>s12</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>positiva</mi><mo>"</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>negativa</mi><mo>"</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>positiva</mi><mo>"</mo><mo>,</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>negativa</mi><mo>"</mo><mo>,</mo><mi>y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>positiva</mi><mo>"</mo><mo>,</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t6</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>"</mo><mi>su</mi><mo> </mo><mi>coordenada</mi><mo> </mo><mo>#</mo><mn>1</mn><mo> </mo><mi>sea</mi><mo> </mo><mi>negativa</mi><mo>"</mo><mo>,</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>t1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>t2</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>t3</mi><mo>,</mo><mn>4</mn><mo>→</mo><mi>t4</mi><mo>,</mo><mn>5</mn><mo>→</mo><mi>t5</mi><mo>,</mo><mn>6</mn><mo>→</mo><mi>t6</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto2</mi><mo>=</mo><mo>"</mo><mi>igual</mi><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>máximo</mi><mo>(</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a2</mi></mfenced><mo>,</mo><mfenced close="⌉" open="⌈"><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a3</mi><mn>2</mn></msup></mrow></msqrt></mfenced><mo>,</mo><mfenced close="|" open="|"><mi>a3</mi></mfenced><mo>)</mo><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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>></mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>z</mi><mo>-</mo><mi>a3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><apply><csymbol 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>y</mi><mo><</mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>z</mi><mo>-</mo><mi>a3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>z</mi><mo>></mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>z</mi><mo>-</mo><mi>a3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow><mrow><mi>test</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>z</mi><mo><</mo><mn>0</mn><mo>∧</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>z</mi><mo>-</mo><mi>a3</mi><msup><mo>)</mo><mn>2</mn></msup><mo>=</mo><msup><mi>d1</mi><mn>2</mn></msup><mo>)</mo><mo>?</mo></mrow></apply></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</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>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>segundo</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>)</mo><mo>?</mo></math></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>2</mn><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_no_more_decimals"><param name="digits">0</param></assertion><assertion name="equivalent_function" correctAnswer="1"><param name="name">test</param></assertion><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">5</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 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¨»«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_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) =