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

>>9
Unlike dot products, cross products are vectors, and that complicates things dramatically.

p = (2,0,0)
q = (1,1,0)
r = (0,2,0)
are clearly collinear, but I don't think any of the 3 cross products are 0 (certainly not p x r)