Thread: linear combinations

The question is:

In a parallelogram ABCD, F is the midpoint of AD, and E divides BC internally in the ratio 3:2. If P is the point of intersection of AE and BF, show that P divides AE in the ratio 5:6.

Okay so do i make combine all these vector ratios into a single vector and then prove the 5:6 ratio? When i do this though, the vectors do not result into a 5:6 ratio. How should I attempt this question?

Let







But the vectors BP and BF are coliniar, then