in a parallelogram OABC vectors a,b,c are respectively the position vectors of vertices A,B,C with reference to O as origin.A point E is taken on the side BC which divides it in the ratio of 2:1.Also,the line segment AE intersects the line bisecting the angle O internally in point P.if CP when extended meets AB in point F, then find

a.the position vector of point P.

b. the position vector of point F

c. ratio in which F divides AB.