What is the norm or <-7 , 5, 1 >?

Dec 7, 2016

$| < - 7 , 5 , 1 > | = 5 \sqrt{3}$

Explanation:

$\setminus \setminus \setminus \setminus \setminus | < - 7 , 5 , 1 > | = | \left(\begin{matrix}- 7 \\ 5 \\ 1\end{matrix}\right) |$
$\therefore | < - 7 , 5 , 1 > | = \left(\begin{matrix}- 7 \\ 5 \\ 1\end{matrix}\right) \cdot \left(\begin{matrix}- 7 \\ 5 \\ 1\end{matrix}\right)$
$\therefore | < - 7 , 5 , 1 > | = \sqrt{{\left(- 7\right)}^{2} + {\left(5\right)}^{2} , + {\left(1\right)}^{2}}$
$\therefore | < - 7 , 5 , 1 > | = \sqrt{49 + 25 + 1}$
$\therefore | < - 7 , 5 , 1 > | = \sqrt{75}$
$\therefore | < - 7 , 5 , 1 > | = \sqrt{25 \cdot 3}$
$\therefore | < - 7 , 5 , 1 > | = 5 \sqrt{3}$