# What is the norm of < -3, -1 , 8 >?

Jan 18, 2016

$\sqrt{74}$

#### Explanation:

For any vector $A = \left({a}_{1} , {a}_{2} , \ldots . , {a}_{n}\right)$ in any finite n-dimensional vector space, the norm is defined as follows :

$| | A | | = \sqrt{{a}_{1}^{2} + {a}_{2}^{2} + \ldots . + {a}_{n}^{2}}$.

So in this particular case we work in ${\mathbb{R}}^{3}$ and get :

$| | \left(\left(- 3 , - 1 , 8\right)\right) | | = \sqrt{{3}^{2} + {1}^{2} + {8}^{2}} = \sqrt{74}$.