Question

Prove that 2 vectors are colinear if and only if v1 x v2 = 0

Answer 1

Let v1 = (x1, y1, z1) and let v2 = (ax1, ay1, az1) where a is a non-zero constant. then v1 and v2 are col;inear. take the cross product and thus if linear, then 0.
to do the other way, take two arbitrary vectors, cross them and set each term equal to 0. Work backwards to show that the original vectors are collinear.

Answer 2

oh yeah, in 2nd part state that the vectors are notthe zero vectors.

Answer 3

if the vectors are collinear they span a degenerate parallelogram between them with area \(0\) :-)