Question

What is the distance between `(–6, 3, 1)` and `(–1, 4, –2)`?

Answer 1

`sqrt(35)`

Explanation:

The (Euclidean) distance between two points `(x_1, y_1, z_1)` and `(x_2, y_2, z_2)` is given by the formula:

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

So for `(x_1, y_1, z_1) = (-6, 3, 1)` and `(x_2, y_2, z_2) = (-1, 4, -2)` the distance is:

`sqrt(((color(blue)(-1))-(color(blue)(-6)))^2+((color(blue)(4))-(color(blue)(3)))^2+((color(blue)(-2))-(color(blue)(1)))^2)`

`=sqrt(5^2+1^2+(-3)^2) = sqrt(25+1+9) = sqrt(35)`