# How do you find the magnitude <3.5, 12>?

Jul 20, 2016

$| | < 3 , 5 , 12 > | | = \sqrt{178} \cong 13.34$.

#### Explanation:

The magnitude of a vector $\vec{x} = \left({x}_{1} , {x}_{2} , {x}_{3}\right)$ is denoted by

$| | \vec{x} | |$ and is defined by,

$| | \vec{x} | | = \sqrt{{x}_{1}^{2} + {x}_{2}^{2} + {x}_{3}^{2}}$

Hence, $| | < 3 , 5 , 12 > | | = \sqrt{9 + 25 + 144} = \sqrt{178} \cong 13.34$.