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.

  • $\begingroup$ Have you tried proof by contradiction? $\endgroup$ Feb 21, 2016 at 6:52
  • $\begingroup$ No I have not, could you explain it? $\endgroup$
    – Drew
    Feb 21, 2016 at 6:57

1 Answer 1


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

  • 1
    $\begingroup$ Don't what have to be two different vectors? $\endgroup$
    – copper.hat
    Mar 21, 2017 at 3:45

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