# A Little Help Vector Calculus Problem

1. Sep 18, 2005

the problem goes:

ABCD is a parallelogram in which points P and Q are the midpoints of sides BC and CD, respectively. Use vector calculus to prove that AP and AQ trisect the diagonal BD at the points E and F.

.....A _________B
....../......F...../
..../...E......../P
D/________/C
........Q
(Imagine lines from D->B, A->Q and A->P, where AQ passes through E and AP passes through F)

I set the Problem Up like this:
DE = x(DA + AB)
EF = y(DA + AB)
FB = z(DA + AB)

After this I get stuck running around in circles trying to make subsitutions to show that x, y & z = 1/3.

Ideas anyone?