# What is the distance between (4, 4, 2) and (5, 6, 4) ?

Mar 15, 2018

The distance between $\left(4 , 4 , 2\right)$ and $\left(5 , 6 , 4\right)$ is $3$ units.

#### Explanation:

We know that in a two dimensional Cartesian plane, distance between points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is

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

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

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

Hence distance between $\left(4 , 4 , 2\right)$ and $\left(5 , 6 , 4\right)$ is

$\sqrt{{\left(5 - 4\right)}^{2} + {\left(6 - 4\right)}^{2} + {\left(4 - 2\right)}^{2}}$

= $\sqrt{1 + 4 + 4} = \sqrt{9} = 3$