Let (V) be a real inner product space. Show that (v perp w) if, and only if,
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Let \(V\) be a real inner product space. Show that \(v \perp w\) if, and only if, Pythagoras' theorem \(\|v+w\|^{2}=\|v\|^{2}+\|w\|^{2}\) holds.
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