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In triangle OAB, #vec ( OA)#=a, #vec (OB)#=b and P lies on AB such that AP: PB=3:5
(a) Find in terms of a and b the vectors
(i) #vec (AB)#
(ii) #vec (AP)#
(iii) #vec (BP)#
(iv) #vec (OP)#
(b) Point Q is on OP such that #AQ= -5/8 a+ 9/40 b#. Find the ratio OQ:QP