> 
> How do I prove that 
>  $$
> \left \|\vec{u} \right \|^2 = \left \|\vec{v} \right \|^2 = \langle\vec{u},\vec{v}\rangle
> $$ if and only if $\vec{u} = \vec{v}$.
> 
> 
> 

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I don't have any idea on how to prove this but I hope some one could help me.