2. Given a = (– 2, 5, 3) and b = (4, 2, — 3). Find the vector projection of a onto b. [2] 3. Use the dot product to find an expression for the cosine of the acute angle between the [4] diagonals of a rectangle with sides a and b. 4. Given the vectors x = (a, 3, 2), y = (1, b, -2) and z = (-11, 7, c) are mutually perpendicular vectors. Find a, b and c. [4] 5. What can you conclude about the vectors of u and v if: a. κ·ν= u · v = |u]]v b. (u xv). u = 0 [6] 6. Find the total work done by a 15 N force, in the direction of vector (1, 2, 2) when it moves a particle from O(0, 0, 0) to R(-2, 4, 0) and then from R to S(11, 1, -1), and then from S to A(7, 2, 5). The distance is measured in metres. [4] 7. If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,-3), B is (4,6,2), and C is (5,0,-2), find the volume of the parallelepiped.