Function in inner product

Question

I really don't even understand this question ( I guess it just a simple one but I don't understand this function given)

Given $V$, an inner product space and function $F\colon V\to V$ such that for every $u,v$ vectors in $V$, $\langle F(u),v\rangle =0$. I need to prove that $F(u)=0$ for each $v\in V$.

Answer 1

Hint. Let $u\in V$. Set $v=F(u)$. The condition $0=\langle F(u),v\rangle$ tells you what about $F(u)$?