Thread: Inner product space problems

1. Inner product space problems

Just started learning it and didn't quite get the hang of it.
So here are the questions:

Let V be an inner product space and $U,W \subseteq{V}$ prove that:
1. a. Solved nvm this one
b. Solved nvm this one
c. $V=U\oplus{W} \Leftrightarrow V=U^\bot \oplus {W^\bot}$

2.In inner product space V we are given { $v_1,....,v_k$} vectors for which
$\|{v}\|^2=(v,v_1)^2+.....+(v,v_k)^2$.
Show that V=span{ $v_1,....,v_k$}

Thanks for any help in advance.