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

Given two points $\left(a , b , c\right)$ and $\left({a}_{1} , {b}_{1} , {c}_{1}\right)$,
d=sqrt((a-a_1)^2+(b-b_1)^2+(c-c_1)^2
$d = \sqrt{{\left(4 - \left(- 1\right)\right)}^{2} + {\left(- 4 - 1\right)}^{2} + {\left(- 2 - 3\right)}^{2}} = \sqrt{{5}^{2} + {5}^{2} + {5}^{2}} = \sqrt{{5}^{2} \left(1 + 1 + 1\right)} = 5 \sqrt{3}$