# What is the distance between (–6, 3, 1)  and (0, 4, –2) ?

Jul 2, 2016

The distance between $\left(- 6 , 3 , 1\right)$ and $\left(0 , 4 , - 2\right)$ is$6.782$

#### Explanation:

In a two dimensional plane, distance between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

and in three dimensional space, distance between two points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by

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

Hence, the distance between $\left(- 6 , 3 , 1\right)$ and $\left(0 , 4 , - 2\right)$ is

$\sqrt{{\left(0 - \left(- 6\right)\right)}^{2} + {\left(4 - 3\right)}^{2} + {\left(- 2 - 1\right)}^{2}}$

= $\sqrt{{6}^{2} + {1}^{2} + {\left(- 3\right)}^{2}} = \sqrt{36 + 1 + 9} = \sqrt{46} = 6.782$