Could anyone help me with the following proof?

Suppose $\displaystyle u,v\in V$. Prove that $\displaystyle <u,v>=0$ if and only if $\displaystyle ||u||\leq ||u+av||$ for all $\displaystyle a\in F$.

I already came up with a proof assuming that $\displaystyle <u,v>=0$ and used the Pythagorean Theorem to prove that $\displaystyle ||u||\leq ||u+av||$.

However, I don't know how to prove it the other way.