Let OA→=a→,OB→=10a→+2b→ and OC→=b→ where O, A and C  are non-collinear points. Let p denote the area of quadrilateral OACB, and let q denote the area of parallelogram with OA and, OC as adjacent sides. If p = k q, then find k.

Here OA→=a→,OB→=10a→+2b→,OC→=b→q : Area of parallelogram with OA and OC as adjacent sides. ∴ q=|a→×b→|-----ip = Area of quadrilateral OABC     = Area of ∆OAB + Area of ∆OBC =12    |a→×(10a→+2b→)|+12|(10a→+2b→)×b→|    =|a→×b→|+5|a→×b→|∴     p=6|a→×b→| or      p=6q∴ k    =6