Question

What is the distance between #(–1, 1, 3) `and`(4, –4, –2)#?

Answer 1

The distance in 3-dimensions is very similar to that in coordinate geometry (2-D).

Given two points `(a,b,c)` and `(a_1,b_1,c_1)`,

`d=sqrt((a-a_1)^2+(b-b_1)^2+(c-c_1)^2`

So,

`d=sqrt((4-(-1))^2+(-4-1)^2+(-2-3)^2)=sqrt(5^2+5^2+5^2)=sqrt(5^2(1+1+1))=5sqrt(3)`