Question

Prove that vectors u , v and w are coplanar if and only if vectors u , v and w are linearly dependent.

Answer 1

I find the best way to look at this is:

If w is in the span of u and v [ i.e. is a linear combination of them]
then u,v,w are linearly dependent

This tells us that u,v,w are 'coplanar', because with the definition of the span and linear dependence, this implies that 'w' is in the plane determined by u,v.

Hope this helps!