Vertices of an equilateral triangle Question: show that the following three points in 3D space A = <-2,4,0>, B = <1,2,-1> C = <-1,1,2> form the vertices of an equilateral triangle.
How do i approach this problem?

Find the distance between all the pairs of points 
$$|AB|,|BC|,|CA|$$
and check if
$$|AB|=|BC|=|CA|$$
For example:
$$|A B| = \sqrt{(-2-1)^2 + (4-2)^2 + (0-(-1))^2} = \sqrt{14}$$
