Is the following theorem true:(adsbygoogle = window.adsbygoogle || []).push({});

Theorem: Suppose [itex]a, \, b \in \mathbb{R}^k[/itex]. If [itex] |a| + |b| = |a + b| [/itex], then [itex] |a| [/itex] and [itex] |b| [/itex] are parallel to each other in the same direction.

I proved the converse, but I couldn't prove the theorem above. Please post the proof or the disproof of it, or a link of them. Thanks.

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# |a+b| = |a| + |b| implies a and b parallel?

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