# What is the distance between (3,2,-1) and (5,-1,6)?

May 1, 2016

$\sqrt{62} \approx 7.874$

#### Explanation:

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

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

$= \sqrt{{\left(5 - 3\right)}^{2} + {\left(- 1 - 2\right)}^{2} + {\left(6 - \left(- 1\right)\right)}^{2}}$

$= \sqrt{{2}^{2} + {\left(- 3\right)}^{2} + {7}^{2}}$

$= \sqrt{4 + 9 + 49}$

$= \sqrt{62} \approx 7.874$