# What is the norm or < 4 , -4 , 9 >?

Jul 11, 2016

$\sqrt{113}$

#### Explanation:

When norm is thought of as a length or distance, we can define the norm of a vector $\vec{u} = \left({u}_{1} , {u}_{2} , \ldots , {u}_{n}\right)$ in n-dimensional space ${\mathbb{R}}^{n}$ as

$| | \vec{u} | | \equiv \sqrt{{u}_{1}^{2} + {u}_{2}^{2} + \ldots + {u}_{n}^{2}}$

In this case, the norm will be given by

$| | \vec{u} | | = \sqrt{{4}^{2} + {\left(- 4\right)}^{2} + {9}^{2}} = \sqrt{113}$