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Multivariable Calculus

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Moderate

Triangle Inequality

MVCALC-BLXKZO

Which of the following statements is NOT always true?

A

$||{\bf u} || +||{\bf v}||\geq ||{\bf u}+{\bf v}||$

B

$||{\bf u} || +||{\bf v}||\geq ||{\bf u}-{\bf v}||$

C

$||{\bf u} || - ||{\bf v}||\geq ||{\bf u} -{\bf v}||$

D

$\large || \cfrac{{\bf u}}{||{\bf u} ||} \large || =\large || \cfrac{{\bf v}}{||{\bf v} ||} \large ||$

E

If ${\bf u}$ and ${\bf v}$ are perpendicular, then ${\bf u} + {\bf v}$ and ${\bf u} - {\bf v}$ have the same length.