# [Math] Evaluating norm of vectors with negative sign

linear algebravectors

Let

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

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

$2\sqrt{966}$
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 $||V||$.