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Let $u$ and $v$ be non-zero vectors in a real inner product space $X.$ Show that $\| u+v \|= \| u\|+\|v\|$ if and only if $v=au,$ for some $a>0.$

I only know the proof for $\|u+v\| ≤ \|u\|+\|v\|.$ How can the equality be established?

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    What part(s) of my answer is (are) not clear to you?2012-04-20

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