If in an inner product space $\langle x,u\rangle=\langle x,v\rangle$ for all $x$, show that $u=v$. If in an inner product space $\langle x,u\rangle=\langle x,v\rangle$ for all $x$, show that $u=v$.
This seems obvious to me, so how do I prove it? Proof by contradiction maybe?
Any suggestions would be nice.

Let $x=u-v$, then:
$$\langle x,u\rangle-\langle x,v\rangle=\langle x,u-v\rangle=\langle u-v,u-v\rangle=0$$
So $u-v=0$.
