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Linear Algebra

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Triangle Equality Condition

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What relationship between two vectors $\vec v,\vec w$ will ensure that the triangle inequality between $\lVert v\rVert$, $\lVert w\rVert$, and $\lVert v+w\rVert$ is an equality?

A

$\langle v,w\rangle=\lVert v\rVert\lVert w\rVert$

B

$\langle v,w\rangle=-\lVert v\rVert\lVert w\rVert$

C

$\langle v,w\rangle=0$

D

$\lVert v\rVert=\lVert w\rVert$

E

$\lVert v\rVert=-\lVert w\rVert$