Question 1: Feb 2022 a) Find x such that the vectors (3,2, x) and (2x,4, x) are orthogonal. b) Find the direction cosines and direction angles of the vector a = 3i-2]-3k . Give the direction angles correct to the nearest degree. c) Consider the parallelepiped with edges AB, AC and AD , where A(1,0,1), B(4,1,3). C(5,a,2) and D(2,2,5). Find the real number, a > 0 such that the volume of the parallelepiped is 45 units. Question 2: Jul 2021 a) Find the value of n if the vectors u = (1, -4, 1), v = (2, n, 1) and w = (0, 2, 1) are coplanar. b) Find the angle between u = (-3, 1, 2) and v = (-2, 3, 1) . Give the answer in two (2) decimal places. c) Let P(-1, 2, 3). Q(5, -2, 3). R(-3, -2, 1) and S(4, 2, 3) be four (4) points in space. Find the volume of parallelepiped determined by the vectors QP , QR and QS