Vectors

Hi i need to prove the following;

3 distinct points, P,Q are R have position vectors p,q and r respectfully. Show that P,Q and R are collinear (that is, all lie on a straight line) if   p x q + q x r + r x p = 0

OP = p
OQ = q
OR = r

p.q + q.r + r.p = 0
|p||q|cosT + |q||r|cosR + |r||p|cosS = 0

because they are all distinct points, that is, they are non-zero vectors, then the only way that we can obtain a sum of 0 is when:
cosT = 0, cosR = 0 and cosS = 0

because all of the angles = 0, then they are all parallel.
and because they all share a common point O, all three points are collinear.