In Diagram 14, the points P and Q have position vectors p and q respectively. OP is produced to R such that OR = 30P and OQ is produced to such that os 400. The lines PS and QR intersect at point T. (a) Express PS and QR in terms of p and q.
(b) Given PT = hPS and OT = kQR, express OT
(i) in terms of h, and q.
(ii) in terms of k, p and q.
(c) Hence, determine the values of h and k.