if $W$ is a subspace of an inner product space $V$, which of the following statements is true? if  $W$ is a subspace of an inner product space $V$, which of the following statements are true?


$1)$ there  is  a unique subspace $W'$ such that $W' + W = V$
$2)$ there  is  a unique subspace $W'$ such that $W'\oplus  W = V$
$3)$ there  is  a unique subspace $ W'$ such that $W' + W = V$ and $\langle w, w '\rangle  = 0 $ for all $w \in  W $  and $w' \in  W' $
$4) $ there  is  a unique subspace $W$' such that $W' \oplus  W = V $ and $ \langle w,w '\rangle $ = $0$ for all $ w \in W$ and $w' \in  W' $


I thinks all options $1,2,3,4 $ will be true  because $W' \cap W = \{0\}$
Any Hints/solution
Thanks u

1) and 2) are not true: you can take any nonorthogonal complement of $W$ as well.
3) the condition implies $W\cap W'=\{0 \}$ so it's the same as 4) which is true in finite dimensions. 
