[Math] Evaluating norm of vectors with negative sign

linear algebravectors


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

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

I get the answer


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

Best Answer

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 $||V||$.

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