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) ?