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QUESTION 1 (a) The points A, B, C and D have coordinates (1, 3, p). (4, 5, 2), (2, 1, -1) and (6, 5, 0) respectively, where p is a constant. 1 (i) Write down the vectors AB AC and AD in term of p. (ii) Show that to be found. AB AC²) · (b) The line / has equation r= The line /2 has equation r = AD Show that PQ is parallel to (3 marks) is of the form m (5-2p), where m is an integer (4 marks) -=+B The point P lies on / where a = -1. The point Q lies on /2 where ß = 2. (i) H (4 marks) (ii) The 41 and 12 intersects at the point R (3, b, c). Show that b = -2 and find the value of c. (4 marks) (iii) The point S lies on a line through P that is parallel to 12. The line RS is perpendicular to line PQ. Calculate the position vector of S. (5 marks) + a 3