4. The diagram is a rectangular prism. Let u = AB, v = AD and w = A. Express each vector as a linear combination of u, v and w. [1 mark each] a) EF = b) HB = E H A D F B G C Completion [1 mark each] Complete each statement. 5. The dot product of any two of the vectors i, j, k is 6. If two vectors are parallel then their dot product equals the product of their 7. An equilibrant vector is the opposite of the 8. The magnitude of vector [a, b, c] is 9. The magnitudes of vector [a, b, c] and vector [-a, - b, - c] are 10. If two vectors are orthogonal then their dot product equals Matching [1 mark each] MNPQ is a parallelogram and R is the intersection point of the diagonals MP and NQ. Let u = MQ and = M MN. Match the following expressions to their equivalents in terms of and v. N A. C. 2 R E. G. u I. ta ta ta ta ta - B. u+v D. - F. -u-v H. 0 J. 2 MR + RQ 11. 12. PQ + QN + 13. MN NP QM 3. If|u| = 3, ||| = 8 and the angle between these vectors is 83, determine a) uxv [2 marks] b) [2 marks] 1. If u = [2,-4, -1] and v = [1, -2, 4] find: a) 3v- u [2 marks] b) +22k| [3 marks] c) Find G, where F(2, -3, 4) and FG = 3 [3 marks] 2. If = [m, n, 1] is perpendicular to both a = [5, 1, 2] and b = [3, -3, 6], find m and n. [3 marks]