Question

What is the distance between `(-2,4,-13)` and `(-4,5,-12)`?

Answer 1

I assume that you know the distance formula (square root of sum of corresponding coordinates squared)
Well, that formula can actually be EXTENDED to the third dimension. (This is a very powerful thing in future mathematics)
What that means is that instead of the known

`sqrt((a-b)^2 + (c-d)^2`

We can extend this to be
`sqrt((a-b)^2 + (c-d)^2 + (e-f)^2`

This problem is beginning to look a lot easier huh?
We can just plug in the corresponding values into the formula

`sqrt((-2--4)^2 + (4-5)^2 + (-13--12)^2`

`sqrt((2)^2 + (-1)^2 + (-1)^2)`

This becomes `sqrt(4 + 1 + 1)`

Which is `sqrt(6)`

This cannot be simplified further, so we are done.