62. A triangle is defined by three points A(0,1,2), B(1,0,2), and C(-1,2,0) . Find the angles ZA, ZB , and ZC of this triangle. 63. Given the vector a = (2,-3,4) , find the scalar projection: a) of a onto the unit vector i b) of a onto the vector i - } c) of a onto the vector b = -i + 2] + k d) of the unit vector i onto the vector a 64. Given two vectors a = (0,1,-2) and b = (-1,0,3) , find: a) the vector projection of the vector a onto the vector b b) the vector projection of the vector b onto the vector a c) the vector projection of the vector a onto the unit vector k d) the vector projection of the vector i onto the vector a 65. The magnitudes of two vectors a and b are | a |=2 and | b |=3 respectively, and the angle between them is a =60 . Find the magnitude of the cross product of these vectors.66. For each case, find the cross product of the vectors a and b. a) a = (1,-2,0), b = (0,-1,2) b) a =-i+2] , b=i-2] -k 67. Use the cross product properties to prove the following relations: a) (a -b)x (a + b) =2(axb) b) (axb) (axb) + (a .b)(a -b)= (a -a)(b .b) 68. Find an unit vector perpendicular to both a = (0,1,1) and b = (1,1,0) . 69. Find the area of the parallelogram defined by the vectors a = (1,-1,0) and b = (0,1,2). 70. Find the area of the triangle defined by the vectors a = (1,2,3) and b = (3,2,1) . 71. Find the volume of the parallelepiped defined by the vectors a = (0,1,1), b = (0,1,0) and c = (1,0,1). 72. Consider the following vectors: a = i + j-k , b =3i -2] , and & =37 -2k . Compute the required operations in terms of the unit vectors i , j , and k . a) a+b b ) a - 26 c ) a .b d) bxc e) (axb)-c f) (axb ) xc g) Proj(a onto b)