Question

What is the distance between `(3, –1, 1)` and `(4, 1, –3)`?

Answer 1

`sqrt(21)`

Explanation:

The 3-D version of the Pythagorean Theorem tells us that that distance between two points `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)` is
`color(white)("XXXXX")sqrt((Deltax)^2+(Delta y)^2+(Delta z)^2)`

`color(white)("XXX")=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

In this case with points `(3,-1,1)` and `(4,1,-3)`
the distance is
`color(white)("XXX")sqrt((4-3)^2+(1-(-1))^2+((-3)-1)^2)`

`color(white)("XXX")=sqrt(1^2+2^2+(-4)^2)`

`color(white)("XXX")=sqrt(21)`