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

Mar 25, 2018

$5 \sqrt{2}$

#### Explanation:

We are given two points in ${\mathbb{R}}^{3}$.

Let's find a vector that connects these two points, then compute the length of that vector.

$\left[3 , - 1 , 1\right] - \left[- 1 , 4 , - 2\right]$

=[(3-(-1), (-1)-4, 1-(-2)]

$= \left[4 , - 5 , 3\right]$

Now the length of this vector is:

$\sqrt{{4}^{2} + {\left(- 5\right)}^{2} + {3}^{2}} = \sqrt{16 + 25 + 9}$

$= \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \sqrt{2} = 5 \sqrt{2}$