What is the distance between #(6, 8, 2) # and # (4, 3, 1) #?

1 Answer
Feb 26, 2016

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 + (8-3)^2 + (2-1)^2#

#sqrt(2^2 + 5^2 + 1^2)#

This becomes #sqrt(4 + 25 + 1)#

Which is #sqrt(30)#

This cannot be simplified further, so we are done.