# What is the distance between  (–2, 1, 3)  and (2, –3, 1) ?

May 4, 2018

$6$

#### Explanation:

The distance between two points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by the formula:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}_{1}\right)}^{2}}$

In our example, putting $\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(- 2 , 1 , 3\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(2 , - 3 , 1\right)$, we find distance:

$d = \sqrt{{\left(2 - \left(- 2\right)\right)}^{2} + {\left(- 3 - 1\right)}^{2} + {\left(1 - 3\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{{4}^{2} + {4}^{2} + {2}^{2}} = \sqrt{36} = 6$