# What is the distance between (6, 8, 2)  and (3, 4, 1) ?

Dec 18, 2015

$\sqrt{26}$

#### Explanation:

Distance between 2 points $\left({x}_{1} , {y}_{1} , {z}_{1}\right)$ and $\left({x}_{2} , {y}_{2} , {z}_{2}\right)$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{\Delta {x}^{2} + \Delta {y}^{2} + \Delta {z}^{2}} = \sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2} + {\left({z}_{1} - {z}_{2}\right)}^{2}}$

For the given points $\left(6 , 8 , 2\right)$ and $\left(3 , 4 , 1\right)$
Distance
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{\left(6 - 3\right)}^{2} + {\left(8 - 4\right)}^{2} + {\left(2 - 1\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{9 + 16 + 1}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{26}$

$\textcolor{w h i t e}{\text{XXX}} \cong 5.099019514$ (using a calculator)