Question

Relative to an origin O, the position vectors of points A,B and C are given by:
-OA=2j-3k
-OB=2i+5j-2k
-OC=3i+pj+qk

(a) In the case where ABC is a straight line, find the values of p and q
(b) In the case where angle BAC is 90°, express q in terms of r
(c) In the case where p=3 and the lengths of AB and BC are equal, find the possible values of q.