Question: I would like to know how the below can be proved. Detailed explanation would be good to have, thanks. 1. Let X be an inner

I would like to know how the below can be proved. Detailed explanation would be good to have, thanks.

1. Let X be an inner product space, and x, y be two non-zero vectors in X. Prove that (a) x, y are orthogonal if and only if lla + ayl| = ||x - ay| for all a E R. (b) x, y are orthogonal if and only if lla + ayl| 2 ||x|| for all a E R

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