Question

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

Answer 1

`sqrt35`

Explanation:

use the 3-dimensional version of the `color(blue)(" distance formula ")`

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2 )`

let `(x_1 , y_1 , z_1 ) = (-2 ,1 , 3)color(black)(" and (x_2 , y_2 , z_2) = (-1 ,4 , -2 )`

substitute these values into the formula.

`d = sqrt((-1+2)^2 + (4 - 1 )^2 + (-2 - 3 )^2)`

`d = sqrt( 1^2 + 3^2 + (-5)^2) = sqrt(1+9+25) = sqrt35`