Question

What is the distance between `(3,5,-2)` and `(-8,5,4)`?

Answer 1

`d=sqrt[157]~~12.53`

Explanation:

Recall the very useful formula to calculate the distance in 2 dimensions i.e: between 2 points:`(x_1,y_1) , (x_2,y_2)`:
`d=sqrt[(x_2-x_1)^2+(y_2-y_1)^2]`

In 3 dimensional space the distance between 3 points is calculated by adding 3rd dimension to the above formula, so now the distance between points:`(x_1,y_1,z_1) , (x_2,y_2,z_2)` is:
`d=sqrt[(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2]`

In this case the points are: `(3,5,−2),(−8,5,4)` so we have:
`d=sqrt[(-8-3)^2+(5-5)^2+(4-(-2))^2]`
`d=sqrt[(-11)^2+(0)^2+(6)^2]`
`d=sqrt[121+0+36]`
`d=sqrt[157]`
`d~~12.53`