Let $V$ an inner product space and $a,b\in V$ prove that $((a,d)=(b,d))\forall d\in V\implies a=b$

Question

I've been working on this problem that required a bi-implication, and one side is pretty simple, but then when I get to the implication in the title, I keep running into problems with circular reasoning. Does anyone here have an idea on how to prove this?

The original question: Let $V$ be an inner product space and let $a, b$ be vectors in $V$. Show that $a=b$ if and only if $(a,d)=(b,d)$ for every $d$ in $V$

Answer 1

Hint:

$$(a,d) = (b,d) \Longleftrightarrow (a-b,d) = 0. $$

There is a special choice of $d$ which makes it clear that $a-b=0$, i.e. $a=b$. (Think about the properties that define an inner product..)