# What is the distance between (7,5,-6) and (-1,6,3)?

Mar 30, 2018

#### Answer:

See a solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2} + {\left(\textcolor{red}{{z}_{2}} - \textcolor{b l u e}{{z}_{1}}\right)}^{2}}$

Substituting the values from the points in the problem gives:

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{6} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{3} - \textcolor{b l u e}{- 6}\right)}^{2}}$

$d = \sqrt{{\left(\textcolor{red}{- 1} - \textcolor{b l u e}{7}\right)}^{2} + {\left(\textcolor{red}{6} - \textcolor{b l u e}{5}\right)}^{2} + {\left(\textcolor{red}{3} + \textcolor{b l u e}{6}\right)}^{2}}$

$d = \sqrt{{\left(- 8\right)}^{2} + {1}^{2} + {9}^{2}}$

$d = \sqrt{64 + 1 + 81}$

$d = \sqrt{146}$

Or

$d \cong 12.083$