Question

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

Answer 1

`2sqrt6`

Explanation:

Using the `color(blue)"3-d version of the distance formula"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2))color(white)(a/a)|)))`
where `(x_1,y_1,z_1)" and " (x_2,y_2,z_2)" are 2 coordinate points."`

Here the 2 points are (-2 ,1 ,3) and (-6 ,3 ,1)

let `(x_1,y_1,z_1)=(-2,1,3)" and " (x_2,y_2,z_2)=(-6,3,1)`

`d=sqrt((-6+2)^2+(3-1)^2+(1-3)^2)`

`=sqrt(16+4+4)=sqrt24==sqrt(4xx6)=2sqrt6`