Question

What is the distance between `(3,15,-2)` and `(-4,15,4)`?

Answer 1

`sqrt(85) approx 9.2195`

Explanation:

Use the three-dimensional distance formula, which can be derived by applying the Pythagorean Theorem twice. Given two points in 3-dimensional space written in rectangular coordinates `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)`, the distance is:

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

For the problem at hand, this becomes

`dist=sqrt(7^2+0^2+6^2)=sqrt(49+36)=sqrt(85) approx 9.2195`.