Intersect extended lines by comparing independent coefficients

Referred to O, A,B,C have position vectors a,b,c. C lies on AB produced with AC:AB=k:1, where 1<k<2. Show $\mathbf c=(1-k)\mathbf a+k\mathbf b$.1 mark

D is the midpoint of OA. Lines DB produced and OC produced meet at E. Given k=3/2, find the position vector of E in terms of a,b and the ratio DB:DE.4 marks