Relate external division, area ratios and a unit-vector projection

Referred to O, $OA=\mathbf a$, $OB=\mathbf b$. C is on AB produced such that 2AB=3BC.

(i) Find OC in terms of a,b.2 marks

(ii) Show that the area of triangle OBC can be written as $k|\mathbf a\times\mathbf b|$, finding k.2 marks

(iii) D is on OB such that area (OAD):area (OBC)=4:3. Find OD in terms of b.3 marks

(iv) Given a,b are unit vectors and angle AOB=60°, find the length of the projection of OC onto OA.3 marks