question: ABCD is a quadrilateral. P,Q,R and S divide AB, AD, CD and CB respectively in the ration 2:1.

(a) Find the position vectors p, q, r, s in therms of a, b, c, d.

(b) Prove that PQRS is a parallelogram.

(a) is easy:

p = (a+2b)/3

q = (a+2d)/3

r = (c+2d)/3

s = (c+2b)/3

But how to do (b) ?