1. The points A, B. C and D have coordinates (2, 1, 3), (4, 1, 5), (2, 5, p) and (q. r, 1) respectively. If AB=CD what are the values of p, g and r? [3] 2. Points A and B have coordinates (2, 1, 1) and (20, -5, 13) respectively. If point C is such that 2AC =CB, what are the coordinates of C? [5] 3. The point P has coordinates (-2, 4, 0). 3 The point Q is such that PQ = -2 The point R has coordinates (-1, 1, r). For which value of / is PQR an equilateral triangle? [5] 4. Point A has coordinates (2, 3, 6). Point B has coordinates (8, 6, 8). Find the point C so that ABand ACare in the same direction and |AC - 77. [6] 5. Forces F, = 1(3i-2j + k) N and F, = /(i+ j+3k) N, where / and , are scalars, act on a box Prove that it is not possible for their resultant force to act in the direction of k. [6] 6. The points P. Q and R have position vectors and (a) Show that the triangle PQR is isosceles. [2] (b) M is the midpoint of QR. Find the position vector of M. [1] (c) Calculate the area of the triangle PQR. [4] -3 -11 7. The points A. B. C and D have position vectors 4 and 20 10 (a) Write down the vector AB. [1] (b) Calculate the length BC (c) Prove that ABCD is a rhombus. [5]