It is given that OP=p and OQ=q. Point A lies on OP such that OA=3/4 OP and point B lies on the extended OQ such that OB=2OQ. The straight line AB meets the straight line PQ at C. If PC =mCQ and AC=nCB, where m and n are positive numbers, express OC in terms of

(a) m, p and q

(b) n, p and q

Hence, determine the value of m and of n. Write down the position vector for C.