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The figure shows triangle OAB in which OA=a and OB=b. Points M and N are on OA and AB respectively such that OM=34OA and AN=23 AB. Lines ON and BM meet at T such that OT=910ON.
(a) Express the following vectors in terms of a and b:
(i) AB
(ii) BM
(iii) ON
(b) Given that BT=kBM, express vector BT in two ways and hence find the value of k.
(c) Express vector TM in terms of a and b.