Vectores 6. Vectores: operatoria y cálculo de coordenadas Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»u«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»v«/mi»«/math» los vectores son los que aparecen en el gráfico:

#graf

Determine las coordenadas «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«/math» de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»u«/mi»«mi»v«/mi»«mn»1«/mn»«/math»:

]]> 1.0000000 0.3333333 0 0 x=#x1y=#y1]]> <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><pi/><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><pi/><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>c1</mi><mo><</mo><mi>c2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>→</mo><mi>a1</mi><mo>,</mo><mn>2</mn><mo>→</mo><pi/><mo>-</mo><mi>a1</mi><mo>,</mo><mn>3</mn><mo>→</mo><pi/><mo>+</mo><mi>a1</mi><mo>,</mo><mn>4</mn><mo>→</mo><mn>2</mn><mo>*</mo><pi/><mo>-</mo><mi>a1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>→</mo><mi>a2</mi><mo>,</mo><mn>2</mn><mo>→</mo><pi/><mo>-</mo><mi>a2</mi><mo>,</mo><mn>3</mn><mo>→</mo><pi/><mo>+</mo><mi>a2</mi><mo>,</mo><mn>4</mn><mo>→</mo><mn>2</mn><mo>*</mo><pi/><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>r1</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>r1</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U2</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>r1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>)</mo><mo>,</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>r1</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>r1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>)</mo><mo>,</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>r1</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o1</mi><mo>=</mo><mi>punto</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>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>o1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>r1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>*</mo><mi>r1</mi><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>altura_ventana</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anchura_ventana</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mostrar_malla</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>falso</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>vector</mi><mo>(</mo><mi>o1</mi><mo>,</mo><mi>U1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>vector</mi><mo>(</mo><mi>o1</mi><mo>,</mo><mi>V1</mi><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>t1</mi><mo>,</mo><mi>u1</mi><mo>,</mo><mi>o1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>anchura_línea</mi><mo>=</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>v1</mi><mo>,</mo><mi>o1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>,</mo><mi>anchura_línea</mi><mo>=</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>r1</mi><mn>2</mn></msup><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>c1</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow><mrow><mi>Re1</mi><mo>=</mo><mi>región</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo><</mo><msup><mfenced><mfrac><mi>r1</mi><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mi>y</mi><mo><</mo><mfrac><msub><mi>U1</mi><mn>2</mn></msub><msub><mi>U1</mi><mn>1</mn></msub></mfrac><mo>*</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>></mo><mn>0</mn></mrow></mfenced></mrow><mrow><mi>Re1</mi><mo>=</mo><mi>región</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo><</mo><msup><mfenced><mfrac><mi>r1</mi><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mi>y</mi><mo>></mo><mfrac><msub><mi>U1</mi><mn>2</mn></msub><msub><mi>U1</mi><mn>1</mn></msub></mfrac><mo>*</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo><</mo><mn>0</mn></mrow></mfenced></mrow></apply></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>c2</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow><mrow><mi>Re2</mi><mo>=</mo><mi>región</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo><</mo><msup><mfenced><mfrac><mi>r1</mi><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mi>y</mi><mo><</mo><mfrac><msub><mi>V1</mi><mn>2</mn></msub><msub><mi>V1</mi><mn>1</mn></msub></mfrac><mo>*</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>></mo><mn>0</mn></mrow></mfenced></mrow><mrow><mi>Re2</mi><mo>=</mo><mi>región</mi><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo><</mo><msup><mfenced><mfrac><mi>r1</mi><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>,</mo><mi>y</mi><mo>></mo><mfrac><msub><mi>V1</mi><mn>2</mn></msub><msub><mi>V1</mi><mn>1</mn></msub></mfrac><mo>*</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo><</mo><mn>0</mn></mrow></mfenced></mrow></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"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>Re1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>transparencia</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>Re2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>,</mo><mi>transparencia</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>9</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>c1</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow><mrow><mi>EU1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>-</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>,</mo><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>-</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow><mrow><mi>EU1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>+</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>,</mo><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>+</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow></apply></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>c2</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>EV1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>-</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>-</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow><mrow><mi>EV1</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>+</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>r1</mi><mo>/</mo><mn>3</mn><mo>*</mo><mi>sen</mi><mo>(</mo><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>+</mo><mi>a1</mi><mo>/</mo><mn>2</mn><mo>)</mo><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>escribir</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>EU1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>escribir</mi><mo>(</mo><mi>a2</mi><mo>,</mo><mi>EV1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tex1</mi><mo>=</mo><mi>caja_de_texto</mi><mo>(</mo><mo>"</mo><mi>u</mi><mo>"</mo><mo>,</mo><mi>U2</mi><mo>,</mo><mo>{</mo><mi>tamaño_fuente</mi><mo>=</mo><mn>18</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tex2</mi><mo>=</mo><mi>caja_de_texto</mi><mo>(</mo><mo>"</mo><mi>v</mi><mo>"</mo><mo>,</mo><mi>V2</mi><mo>,</mo><mo>{</mo><mi>tamaño_fuente</mi><mo>=</mo><mn>18</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>tex1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t1</mi><mo>,</mo><mi>tex2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><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">repeat</csymbol><mtable><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>R3</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>"</mo><mi>u</mi><mo>+</mo><mi>v</mi><mo>"</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>"</mo><mi>u</mi><mo>-</mo><mi>v</mi><mo>"</mo><mo>,</mo><mn>3</mn><mo>→</mo><mo>"</mo><mi>v</mi><mo>-</mo><mi>u</mi><mo>"</mo><mo>,</mo><mn>4</mn><mo>→</mo><mo>"</mo><mo>-</mo><mi>u</mi><mo>-</mo><mi>v</mi><mo>"</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>R4</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>U1</mi><mo>+</mo><mi>V1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>U1</mi><mo>-</mo><mi>V1</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>V1</mi><mo>-</mo><mi>U1</mi><mo>,</mo><mn>4</mn><mo>→</mo><mo>-</mo><mi>U1</mi><mo>-</mo><mi>V1</mi><mo>}</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>R4</mi><mo>(</mo><mi>w1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></mtd></mtr></mtable><mrow><mi>x1</mi><mo>≠</mo><mn>0</mn><mo>∨</mo><mi>y1</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>uv1</mi><mo>=</mo><mi>R3</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>(</mo><mi>c1</mi><mo>)</mo><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>(</mo><mi>c2</mi><mo>)</mo><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>,</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></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><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U1</mi><mn>1</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>U1</mi><mn>2</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></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><mrow><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>,</mo><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>PM1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><msqrt><mn>3</mn></msqrt></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 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></math>]]></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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="inputField">popupEditor</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>