Question

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

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

`sqrt((-10)^2 + (4)^2 + (2)^2)`

`sqrt(100 + 16 + 4)`

`sqrt(120)`

which is equal to `2sqrt30`

And we are done.