Question

What is the distance between `(-2,-1,-7)` and `(11,5,-3)`?

Answer 1

`sqrt221~~14.87" to 2 dec. places"`

Explanation:

`"using the 3-dimensional version of the "color(blue)"distance formula"`

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

`"let "(x_1,y_1,z_1)=(-2,-1,-7)" and "`

`(x_2,y_2,z_2)=(11,5,-3)`

`d=sqrt((11+2)^2+(5+1)^2+(-3+7)^2)`

`color(white)(d)=sqrt(169+36+16)=sqrt221~~14.87`

Answer 2

`AB=sqrt(221)`

Explanation:

We know that,

If `AinRR^3 and BinRR^3` then the distance between

`A(x_1,y_1,z_1) and B(x_2,y_2,z_2)`, is

`AB=|vec(AB)|=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

Where, `vec(AB)=(x_2-x_1,y_2-y_1,z_2-z_1)`.

We have,

`A(-2,-1,-7) andB(11,5,-3)`

So,

`AB=sqrt((11+2)^2+(5+1)^2+(-3+7)^2)`

`AB=sqrt(169+36+16)`

`AB=sqrt(221)`