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

Mar 8, 2016

$13.565$

#### 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

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

Hence distance between (1,3,−6) and (−5,1,6) is

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

$\sqrt{{\left(- 6\right)}^{2} + {\left(- 2\right)}^{2} + {\left(6 + 6\right)}^{2}}$ or

$\sqrt{36 + 4 + 144}$ or $\sqrt{184}$ or $13.565$