Question

What is the distance between `(0, 0, 8)` and `(8, 6, 2)`?

Answer 1

`2sqrt(34)` units.

Explanation:

The distance formula for Cartesian coordinates is

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`
Where `x_1, y_1,z_1`, and`x_2, y_2,z_2` are the Cartesian coordinates of two points respectively.
Let `(x_1,y_1,z_1)` represent `(0,0,8)` and `(x_2,y_2,z_2)` represent `(8,6,2)`.
`implies d=sqrt((8-0)^2+(6-0)^2+(2-8)^2`
`implies d=sqrt((8)^2+(6)^2+(-6)^2`
`implies d=sqrt(64+36+36`
`implies d=sqrt(136`
`implies d=2sqrt(34` units

Hence the distance between the given points is `2sqrt(34)` units.