I read that three vectors in $\mathbb R^3$ are coplanar if one is a linear combination of the other two. I tried to prove this statement but couldn't do it.
I know that three vectors $\mathbf u,\,\mathbf v,\,\mathbf w \in \mathbb R^3$ are complanar if and only if $$\mathbf u \cdot (\mathbf v \times \mathbf w) = 0.$$
Can I use this fact to prove the above statement? Also is the statement an "if" or an "if and only if"?