# What is ||<< -6,-7,1 >>|| (the magnitude of << -6, -7, 1 >>)?

Dec 29, 2015

Well, the magnitude of an $N$-dimensional vector is determined via an "expanded" form of the Pythagorean Theorem:

$\setminus m a t h b f \left(| | \left\langle{n}_{1} , {n}_{2} , \ldots , {n}_{N}\right\rangle | | = \sqrt{{n}_{1}^{2} + {n}_{2}^{2} + \ldots + {n}_{N}^{2}}\right)$

where $n$ is a specific dimension (like $x$, $y$, or $z$), and $N$ is the number of dimensions.

To get the magnitude of this vector:

$| | \left\langle- 6 , - 7 , 1\right\rangle | |$

$= \sqrt{{\left(- 6\right)}^{2} + {\left(- 7\right)}^{2} + {1}^{2}} = \sqrt{86}$

$\approx \textcolor{b l u e}{9.2736}$