# Inner Product and projection

V is in inner product space over F and U is subspace. $p=P_u(v)$. I need to prove or disprove by an example that:

1. $||v||=||p||$

2. $<v,p>=<p,p>$

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You need to prove/disprove, we need your attempt. – Davide Giraudo Dec 4 '12 at 21:40
What inner product spaces come to mind? – Rudy the Reindeer Dec 4 '12 at 21:41
I dont know where to start so can u please guide me? im not looking for solution – baaa12 Dec 4 '12 at 21:43
I am guiding: what inner product spaces do you know? – Rudy the Reindeer Dec 4 '12 at 21:46
can you help me in what ||p|| is?? – baaa12 Dec 4 '12 at 22:01

Hint: ad 1. What do you know about $\ker P_U$? Can a $v\in\ker P_U$ fulfill 1.?
ad 2. What does it mean for $P_U$ to be an orthogonal projection? Can you say something about $P_U(v-p)$?