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Let

$U = (-2,-1,4,5) \quad V = (3,1,-5,7)$

What is $ \; ||-||U||V|| $ ?

I get the answer

$2\sqrt{966}$

Which is correct, but with this, I assume that the negative is ignored. Can anyone explain why the negative gets thrown out?

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    In your question, is the norm denoted $|U|$ or as $||U||$? Either way it seems something is off in the expression after "What is". – 2017-01-09
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    @coffeemath: It seems it is supposed to be parsed as $\bigl\|-(\|U\|)V\bigr\|$, as in seeker's answer. – 2017-01-09
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    Remember that one of the properties of a norm is that $\|\alpha v\|=|\alpha|\|v\|$ for every scalar $\alpha$. Thus $$\|(-\|U\|)V\|=|-\|U\||\|V\|=\|U\|\|V\|$$ – 2017-01-09

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We get $||U||=\sqrt{46}$, so now we need to calculate $||-\sqrt{46}(3,1,-5,7)||=\sqrt{(-\sqrt{46}\cdot 3)^2+...+(-\sqrt{46\cdot 7})^{2}}=\sqrt{3864}=2\sqrt{966}$.

The reason there is no negative is because you are squaring it for calculating $||V||$.