Matemáticas I Bisectrices de un triángulo. INCENTRO Resolución. Cloze. Dada el triángulo con vértices A #A ,B#B y C#C .Realiza el siguiente procedimiento (escribe las ecuaciones de las rectas pedidas en su forma pendiente-ordenada al origen, es decir, despejada la y):

1. Determina la ecuación de la bisectriz r correspondiente al vértice A: {#1}

2. Determina la ecuación de la bisectriz s correspondiente al vértice B: {#2}

3. Determina la ecuación de la bisectriz p correspondiente al vértice C: {#3}

4. Determina el INCENTRO del triángulo (recuerda escribir las coordenadas entre corchetes): {#4}

#dib

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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><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> Funciones trigonométricas básicas Relaciona cada función con la gráfica correspondiente.

]]> 1.0000000 0.1000000 0 true #gra1

]]> f(x)=#f1 #gra2

]]> f(x)=#f2 #gra3

]]> f(x)=#f3 #gra4

]]> f(x)=#f4 #gra5

]]> f(x)=#f5 #gra6

]]> f(x)=#f6 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t3</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t4</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t5</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><mo>;</mo><mi>t6</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo><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><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>sec</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>csc</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f6</mi><mo>=</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>cot</mi><mo>(</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra1</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra2</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t2</mi><mo>,</mo><mi>f2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra3</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t3</mi><mo>,</mo><mi>f3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra4</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t4</mi><mo>,</mo><mi>f4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra5</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t5</mi><mo>,</mo><mi>f5</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gra6</mi><mo>=</mo><mi>representar</mi><mo>(</mo><mi>t6</mi><mo>,</mo><mi>f6</mi><mo>)</mo></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Matemáticas II Interpretación geométrica del producto mixto. Resolución. Cloze. Interpretación geométrica del producto mixto.

Volumen del paralelepípedo:

El valor absoluto del producto mixto representa el volumen del paralelepípedo cuyas aristas son tres vectores AB, AC, AD que concurren en un mismo vértice A.

El volumen del tetraedro: Es un sexto del volumen del paralepípedo.

Sabiendo las coordenadas de los puntos A, B ,C, D.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»z«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»z«/mi»«mn»2«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»3«/mn»«mo»,«/mo»«mo»#«/mo»«mi»z«/mi»«mn»3«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»D«/mi»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»x«/mi»«mn»4«/mn»«mo»,«/mo»«mo»#«/mo»«mi»y«/mi»«mn»4«/mn»«mo»,«/mo»«mo»#«/mo»«mi»z«/mi»«mn»4«/mn»«mo»)«/mo»«/math»

Hallar :

El Volumen del paralepípedo =

{#1}

El volumen del tetraedro=

{#2}

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>z4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>x1</mi><mo>≠</mo><mi>x2</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>x1</mi><mo>≠</mo><mi>x3</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>x1</mi><mo>≠</mo><mi>x4</mi><mo>∧</mo><mo> </mo><mi>x2</mi><mo>≠</mo><mi>x3</mi><mo>∧</mo><mo> </mo><mi>x2</mi><mo>≠</mo><mi>x4</mi><mo>∧</mo><mo> </mo><mi>x3</mi><mo>≠</mo><mi>x4</mi><mo>)</mo></mrow></apply></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Punto</mi><mo> </mo><mi>A</mi></math></comment></maction><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><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo><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><mn>6</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><mo>-</mo><mo> </mo><mn>2</mn><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Punto</mi><mo> </mo><mi>B</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo> </mo><mo>=</mo><mo> </mo><mn>4</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><mn>12</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><mo>-</mo><mo> </mo><mn>4</mn><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Punto</mi><mo> </mo><mi>C</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo> </mo><mo>=</mo><mo> </mo><mn>10</mn><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><mo>-</mo><mo> </mo><mn>6</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><mo>-</mo><mo> </mo><mn>4</mn><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Punto</mi><mo> </mo><mi>D</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo> </mo><mo>=</mo><mo> </mo><mo> </mo><mn>2</mn><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y4</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mo> </mo><mn>3</mn><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z4</mi><mo> </mo><mo>=</mo><mo> </mo><mn>8</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>punto</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mo> </mo><mi>y1</mi><mo>,</mo><mo> </mo><mi>z1</mi><mo>)</mo><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>punto</mi><mo>(</mo><mi>x2</mi><mo>,</mo><mo> </mo><mi>y2</mi><mo>,</mo><mo> </mo><mi>z2</mi><mo>)</mo><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>punto</mi><mo>(</mo><mi>x3</mi><mo>,</mo><mo> </mo><mi>y3</mi><mo>,</mo><mo> </mo><mi>z3</mi><mo>)</mo><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>punto</mi><mo>(</mo><mi>x4</mi><mo>,</mo><mo> </mo><mi>y4</mi><mo>,</mo><mo> </mo><mi>z4</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AB</mi><mo> </mo><mo>=</mo><mo> </mo><mi>vector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mo> </mo><mi>B</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AC</mi><mo> </mo><mo>=</mo><mo> </mo><mi>vector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mo> </mo><mi>C</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AD</mi><mo> </mo><mo>=</mo><mo> </mo><mi>vector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mo> </mo><mi>D</mi><mo>)</mo><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Volumen</mi><mo> </mo><mi>de</mi><mo> </mo><mi>paralepipedo</mi><mo>:</mo><mi>V</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfenced close="|" open="|"><apply><scalarproduct/><mrow><mi>AB</mi><mo> </mo><mo>×</mo><mo> </mo><mi>AC</mi></mrow><mrow><mo> </mo><mi>AD</mi></mrow></apply></mfenced></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><mfenced close="|" open="|"><mfenced close="|" open="|"><mtable><mtr><mtd><mo>(</mo><mi>x2</mi><mo>-</mo><mi>x1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>y2</mi><mo>-</mo><mi>y1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>z2</mi><mo>-</mo><mi>z1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mo>(</mo><mi>x3</mi><mo>-</mo><mi>x1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>y3</mi><mo>-</mo><mi>y1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>z3</mi><mo>-</mo><mi>z1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mo>(</mo><mi>x4</mi><mo>-</mo><mi>x1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>y4</mi><mo>-</mo><mi>y1</mi><mo>)</mo></mtd><mtd><mo>(</mo><mi>z4</mi><mo>-</mo><mi>z1</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2556</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>≠</mo><mi>V</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Volumen</mi><mo> </mo><mi>de</mi><mo> </mo><mi>tetraedro</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mfenced close="|" open="|"><apply><scalarproduct/><mrow><mi>AB</mi><mo> </mo><mo>×</mo><mo> </mo><mi>AC</mi></mrow><mrow><mo> </mo><mi>AD</mi></mrow></apply></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>426</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>≠</mo><mi>x</mi></math></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> Matriz inversa Calcula la matriz inversa de #m

]]> Recuerda que la matriz tiene inversa si el determinante es distinto de cero.

]]> 1.0000000 0.1000000 0 0 #sol Muy bien!

]]> <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>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</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><mrow><mi>m</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></mrow><mrow><mfenced close="|" open="|"><mi>m</mi></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></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><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>3</mn></mtd></mtr></mtable></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"><mfenced><mtable><mtr><mtd><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></mtd><mtd><mfrac><mn>2</mn><mn>9</mn></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>-</mo><mfrac><mn>4</mn><mn>27</mn></mfrac></mtd><mtd><mo>-</mo><mfrac><mn>1</mn><mn>27</mn></mfrac></mtd><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>*</mo><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><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> POSICION RELATIVA DE TRES PLANOS Estudiar la posición relativa de los siguientes planos:

x-y+z=2

x+y-3z=4

3x-y-z=-3

]]> 1.0000000 0.1000000 0 true true none Los planos forman un prisma

]]> Los planos son paralelos

]]> Se cortan en un punto.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>3</mn><mi>z</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rango</mi><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>(</mo><mi>C</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo> </mo><mi>R</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo> </mo><mo> </mo><mi>Sistema</mi><mo> </mo><mi>incompatible</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Como</mi><mo> </mo><mi>no</mi><mo> </mo><mi>hay</mi><mo> </mo><mi>dos</mi><mo> </mo><mi>planos</mi><mo> </mo><mi>paralelos</mi><mo>,</mo><mo> </mo><mi>los</mi><mo> </mo><mi>tres</mi><mo> </mo><mi>planos</mi><mo> </mo><mi>forman</mi><mo> </mo><mi>una</mi><mo> </mo><mi>superficie</mi><mo> </mo><mi>prismática</mi><mo>.</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero3d</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>12</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>12</mn></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar3d</mi><mo>(</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>z</mi><mo>=</mo><mn>2</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>rojo</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar3d</mi><mo>(</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>3</mn><mi>z</mi><mo>=</mo><mn>4</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>azul</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar3d</mi><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verde</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>;</mo></math></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>