# What is the norm of < -5 , -2, -1 >?

Dec 25, 2015

$\sqrt{30}$

#### Explanation:

By definition, for any n-dimensional vector $A = \left({a}_{1} , {a}_{2} , {a}_{3} , \ldots \ldots , {a}_{n}\right)$, the norm is defined by
$| | A | | = \sqrt{{a}_{1}^{2} + {a}_{2}^{2} + {a}_{3}^{2} + \ldots \ldots . . + {a}_{n}^{2}}$.

So in this particular case we have a 3 dimensional vector (n = 3), and so its norm is given by

$| | \left(- 5 , - 2 , - 1\right) | | = \sqrt{{\left(- 5\right)}^{2} + {\left(- 2\right)}^{2} + {\left(- 1\right)}^{2}}$

$= \sqrt{30}$