El resultado de u → × v → \overrightarrow{\ u}\ \times\ \overrightarrow{\ v} u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> × v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> es ....

Depende de u → \overrightarrow{\ u} u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> y de v → \overrightarrow{\ v} v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

u → × v → \overrightarrow{\ u}\ \times\overrightarrow{\ v}\ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> × v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> es igual a …

... el área del paralelogramo que forman u → \overrightarrow{\ u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> y v → \overrightarrow{\ v} v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

... el área del triángulo que forman u → \overrightarrow{\ u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> y v → \overrightarrow{\ v} v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

... un vector paralelo a u → \overrightarrow{u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> y v → \overrightarrow{v} v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

Sea u → = ( 2 , − 1 , 3 ) \overrightarrow{\ u}=\left(2,-1,3\right) u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> = ( 2 , − 1 , 3 )

( − 4 , 2 , − 6 ) \left(-4,2,-6\right) ( − 4 , 2 , − 6 ) es paralelo a u → \overrightarrow{\ u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

( − 2 , 1 , − 3 ) \left(-2,1,-3\right) ( − 2 , 1 , − 3 ) es perpendicular a u → \overrightarrow{\ u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

Su módulo vale 11 \sqrt{11} 1 1 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

¿Cuál de las siguientes igualdades NO es correcta? ( α \alpha α es el ángulo que forman u → \overrightarrow{\ u} u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> y v → \overrightarrow{v\ } v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> )

u → . v → = ∣ u → ∣ . ∣ v → ∣ . s e n α \overrightarrow{\ u}.\ \overrightarrow{v\ }=\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|.\ sen\ \alpha u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> . v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> = ∣ ∣ ∣ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ . ∣ ∣ ∣ v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ . s e n α

∣ u → × v → ∣ = ∣ u → ∣ . ∣ v → ∣ . s e n α \left|\overrightarrow{\ u}\times\overrightarrow{\ v}\right|=\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|.\ sen\ \alpha ∣ ∣ ∣ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> × v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ = ∣ ∣ ∣ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ . ∣ ∣ ∣ v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ . s e n α

cos ⁡ α = u → . v → ∣ u → ∣ . ∣ v → ∣ \cos\ \alpha=\frac{\overrightarrow{\ u}.\ \overrightarrow{v\ }}{\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|} cos α = ∣ ∣ ∣ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ . ∣ ∣ ∣ v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> ∣ ∣ ∣ u <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" /> . v <path d="M 0 241 v 40 h 399891 c -47.3 35.3 -84 78 -110 128 c -16.7 32 -27.7 63.7 -33 95 c 0 1.3 -0.2 2.7 -0.5 4 c -0.3 1.3 -0.5 2.3 -0.5 3 c 0 7.3 6.7 11 20 11 c 8 0 13.2 -0.8 15.5 -2.5 c 2.3 -1.7 4.2 -5.5 5.5 -11.5 c 2 -13.3 5.7 -27 11 -41 c 14.7 -44.7 39 -84.5 73 -119.5 s 73.7 -60.2 119 -75.5 c 6 -2 9 -5.7 9 -11 s -3 -9 -9 -11 c -45.3 -15.3 -85 -40.5 -119 -75.5 s -58.3 -74.8 -73 -119.5 c -4.7 -14 -8.3 -27.3 -11 -40 c -1.3 -6.7 -3.2 -10.8 -5.5 -12.5 c -2.3 -1.7 -7.5 -2.5 -15.5 -2.5 c -14 0 -21 3.7 -21 11 c 0 2 2 10.3 6 25 c 20.7 83.3 67 151.7 139 205 Z m 0 0 v 40 h 399900 v -40 Z" />

¿Qué afirmación es falsa ?

Todas las afirmaciones son ciertas.

Dos vectores proporcionales son paralelos

Si el producto escalar de dos vectores es 0, son ortogonales

Al dividir las coordenadas de un vector entre su módulo, se convierte en unitario, es decir, el módulo vale 1.

Vectores en el espacio I

Authored by Pablo Correa Gordillo

Mathematics

12th Grade

Used 35+ times

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¿Cuál de las siguientes igualdades NO es correcta?
( $\alpha$ es el ángulo que forman $\overrightarrow{\ u}$ y $\overrightarrow{v\ }$ )

\left|\overrightarrow{\ u}\times\overrightarrow{\ v}\right|=\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|.\ sen\ \alpha

$\overrightarrow{\ u}.\ \overrightarrow{v\ }=\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|.\ sen\ \alpha$

$\cos\ \alpha=\frac{\overrightarrow{\ u}.\ \overrightarrow{v\ }}{\left|\overrightarrow{\ u}\right|.\ \left|\overrightarrow{\ v}\right|}$

Todas las igualdades son correctas

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Vectores en el espacio I

El resultado de u→ × v→\overrightarrow{\ u}\ \times\ \overrightarrow{\ v} u × v es ....

Si dos vectores son paralelos ....

La operación u→ × v→ × w→\overrightarrow{\ u}\ \times\overrightarrow{\ v}\ \times\overrightarrow{\ w} u × v × w ...

u→ × v→ \overrightarrow{\ u}\ \times\overrightarrow{\ v}\ u × v es igual a …

Sea u→=(2,−1,3)\overrightarrow{\ u}=\left(2,-1,3\right) u=(2,−1,3)

( u→. v→)+( u→× v→)\left(\overrightarrow{\ u}.\ \overrightarrow{\ v}\right)+\left(\overrightarrow{\ u}\times\overrightarrow{\ v}\right)( u. v)+( u× v) da como resultado....

Para calcular el ángulo entre dos vectores usamos...

De la operación u →. v →. w→ . x →. y→\overrightarrow{\ u\ }.\ \overrightarrow{\ v\ }.\ \overrightarrow{\ w}\ .\ \overrightarrow{\ x\ }.\ \overrightarrow{\ y} u . v . w . x . y​ se obtiene...

El punto medio de A=(1,2,-5) y B=(1, 0,2) es

¿Cuál de las siguientes igualdades NO es correcta?( α\alphaα es el ángulo que forman u→\overrightarrow{\ u} u y v →\overrightarrow{v\ }v )

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El resultado de $\overrightarrow{\ u}\ \times\ \overrightarrow{\ v}$ es ....

La operación $\overrightarrow{\ u}\ \times\overrightarrow{\ v}\ \times\overrightarrow{\ w}$ ...

$\overrightarrow{\ u}\ \times\overrightarrow{\ v}\$ es igual a …

Sea $\overrightarrow{\ u}=\left(2,-1,3\right)$

$\left(\overrightarrow{\ u}.\ \overrightarrow{\ v}\right)+\left(\overrightarrow{\ u}\times\overrightarrow{\ v}\right)$ da como resultado....

De la operación $\overrightarrow{\ u\ }.\ \overrightarrow{\ v\ }.\ \overrightarrow{\ w}\ .\ \overrightarrow{\ x\ }.\ \overrightarrow{\ y}$ se obtiene...

¿Cuál de las siguientes igualdades NO es correcta?
( $\alpha$ es el ángulo que forman $\overrightarrow{\ u}$ y $\overrightarrow{v\ }$ )