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The points P,Q, R and S have position vectors 2p, 3p,r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6.
(a) Find in the simplest form the vectors OT and QT in terms of p and r
(b)(i) Show that the point Q,T and R lie on a straight line
(ii) Determine the ratio in which T divides QR