What is the distance between (3,13,10) and (3,-17,-1)?

Apr 7, 2016

Distance between $\left(3 , 13 , 10\right)$ and $\left(3 , - 17 , - 1\right)$ is $31.95$ units.

Explanation:

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 $\left(3 , 13 , 10\right)$ and $\left(3 , - 17 , - 1\right)$ is

$\sqrt{{\left(3 - 3\right)}^{2} + {\left(\left(- 17\right) - 13\right)}^{2} + {\left(\left(- 1\right) - 10\right)}^{2}} = \sqrt{{\left(0\right)}^{2} + {\left(- 17 - 13\right)}^{2} + {\left(- 1 - 10\right)}^{2}}$

= $\sqrt{{\left(0\right)}^{2} + {\left(- 30\right)}^{2} + {\left(- 11\right)}^{2}} = \sqrt{0 + 900 + 121}$

= $\sqrt{1021} = 31.95$