JEE Advance - Mathematics (1989 - No. 6)

In a triangle $$OAB,E$$ is the midpoint of $$BO$$ and $$D$$ is a point on $$AB$$ such that $$AD:DB=2:1.$$ If $$OD$$ and $$AE$$ intersect at $$P,$$ determine the ratio $$OP:PD$$ using vector methods.