Prove that if $V$ and $W$ are orthogonal subspaces, then $V \cap W=\{0\}$

Question

I am having issues with this problem:

If $V$ and $W$ are orthogonal subspaces then prove that $V \cap W=\{0\}$

I have tried many methods and techniques but I keep getting it wrong.

Answer 1

Suppose $v \in V \cap W$. Then $v \bot v$, or $\langle v , v \rangle = \|v\|^2 = 0$ and so $v = 0$.