12. [-/1 Points] DETAILS LARCALCET7 11.4.036. MY NOTES ASK YOUR TEACHER Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w. u = (1, 3, 1) V = (0, 6, 6) W = (-4, 0, -4) A 6 8* * W9. [-/2 Points] DETAILS LARCALCET7 11.3.039. MY NOTES ASK YOUR TEACHER Consider the following. u = 8i + 5j, v = 2i + 3j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v. 10. [-/3 Points] DETAILS LARCALCET7 11.4.009. MY NOTES ASK YOUR TEACHER Find u x v, v x u, and v x v. u = (8, -9, 9) V = (-1, 6, -6) ( a ) uxv (b) vxu (c) v xV 11. [-/1 Points] DETAILS LARCALCET7 11.4.021. MY NOTES ASK YOUR TEACHER Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u = (7, 3, -1) V = (1, 3, 7 )6. [-/5 Points] DETAILS LARCALCET7 11.3.010. MY NOTES ASK YOUR TEACHER Find u . v, u . u, ||v||2, (u . v)v, and u . (3v). u = 9i + j - 2k, v = i - 2j + 6k (a) u . v ( b) u . u (c) (d ) ( u . v ) v (e) u . (3v) 7. [-/2 Points] DETAILS LARCALCET7 11.3.018. MY NOTES ASK YOUR TEACHER Find the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to three decimal places and part (b) to one decimal place. ) u = 2i - 9j + k v = i - 2j + k (a) radians 0 = (b) degrees 0 = 8. [-/6 Points] DETAILS LARCALCET7 11.3.031. MY NOTES ASK YOUR TEACHER Find the direction cosines and angles of u and show that cos a + cos B + cosy = 1. (Round your answers for the angles to four decimal places.) u = i + 8j + 4k COS a = a = rad COS B = B = rad cos Y rad1. [-/4 Points] DETAILS LARCALCET7 11.2.029. MY NOTES ASK YOUR Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. A (4, -1, -1), B ( 2 , 0 , -4 ) , C ( 3 , 5 , - 1 ) |AB| = |ACI = IBC| = right triangle isosceles triangle neither 2. [-/3 Points] DETAILS LARCALCET7 11.2.051. MY NOTES ASK YOUR TEACHER Find the component form and magnitude of the vector v with the given initial and terminal points. Then find a unit vector in the direction of v. Initial point: (4, 6, 0) Terminal point: (4, 1, 8) 3. [-/1 Points] DETAILS LARCALCET7 11.2.072. MY NOTES ASK YOUR TEACHER Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (-7, -3, -2), (-5, 0, -9), (3, 4, -4) The given points form the vertices of a parallelogram. O The given points do not form the vertices of a parallelogram.4. [-/4 Points] DETAILS LARCALCET7 11.1.027. MY NOTES ASK YOUR TEACHER Find zu, 3v, v - u, and 2u + 5v. u = (5, 9), V = (3, -6) (a ) (b) 3v (C v - u (d) 2u + 5v 5. [-/6 Points] DETAILS LARCALCET7 11.1.041. MY NOTES ASK YOUR TEACHER Find the following. u = ( 1, 4 ), V = ( 2 , 3 ) (a) lull (b ) utvll (d) (e) (f ) u + v u + vil