Question

What is the distance between `(3,-1,-5)` and `(4,-3,6)`?

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((3-4)^2 + (-1-(-3))^2 + (-5-6)^2`

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

This becomes `sqrt(1 + 4 + 121)`

Which is `sqrt(126)`

This is equal to `3sqrt(14)`

This cannot be simplified further, so we are done.