9. U = 22 V = 13 Q = 71 degrees Uxv = ? , ux v = lu| x |u| x cos(0) U x v = 22 x 13 x cos (71 degrees) = 286 cos(71 degrees) = 93.11 10. The given vectors U = [8, -3, 4] V = [-2, 9,1] W = [0, -1, 7] V = lu * (v * w)I V * W = [ Vy x Wz - Vz x Wy, Vz x - Vx x Wz, Vx x Wy - Vy X Wx] = [97 - 1(-1), 1x0 - (-2) x 7, (-2)(-1) - 9 x 0] = [63 + 1, 0 + 14, 2] = [64, 14, 2] U * (v x W) = 8 x 64+(-3) x 14 + 4 x2 = 512 - 42 +8 = 478 lu * (v x w)| = |478| = 478 cubic units 11. Given info force = [10, 13] newtons Displacement = [8, -1] Work = force * displacement = [10, 13] * [8,-1] =(10 x 8) + (13 x - 1) = 80 - 13 = 67 Work done = 67 joules(J)\f14. Find the vector and scalar equations for the plane through A(1. 0, 10), B(5, -5, 3), and C(8, 8, 2). [6 marks] o 9. If U has a magnitude of 22 and U has a magnitude of 13, and the angle between them is 71, find the dot product of w and v. [2 marks] _:'. 10. Find the volume of the parallelepiped defined by the vectors U = 8, -3,4].v=[-2,9,1]. and _:'. w = [0, 1, 7). [4 marks] 11. A force of [10,13] Newtons acts on an object as it moves along the displacement [8,-1] metres. Find the work done. [3 marks]