# What is the distance between (4,2,6) and (7,3,6)?

Apr 12, 2018

$\sqrt{10}$ units

#### Explanation:

The distance, $\left(D\right)$ between two points in 3-space $\left({x}_{1} , {y}_{1} , {z}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2} , {z}_{2}\right)$ is given by:

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

In this example: ${x}_{1} = 4 , {y}_{1} = 2 , {z}_{1} = 6 \mathmr{and} {x}_{2} = 7 , {y}_{2} = 3 , {z}_{2} = 6$

Hence, $D = \sqrt{{\left(4 - 7\right)}^{2} + {\left(2 - 3\right)}^{2} + {\left(6 - 6\right)}^{2}}$

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

$= \sqrt{9 + 1 + 0}$

$= \sqrt{10}$ units