Question

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

Answer 1

`2sqrt2`

Explanation:

`color(blue)((6,8,2) and (8,6,2)`

Use the `"3-dimensional"` Distance formula

`color(brown)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

Where

`color(indigo)(d="distance"`

So,

`color(indigo)(underbrace("(6,8,2) and (8,6,2)")_((x_1,y_1,z_1) and (x_2,y_2,z_2))`

`color(violet)(x_1=6,x_2=8`

`color(violet)(y_1=8,y_2=6`

`color(violet)(z_1=2,z_2=2`

`rarrd=sqrt((8-6)^2+(8-6)^2+(2-2)^2)`

`rarrd=sqrt((2)^2+(2)^2+(0)^2)`

`rarrd=sqrt(4+4+0)`

`color(green)(rArrd=sqrt(8)=sqrt(4*2)=2sqrt2`