Show that the points
(a,b,c,)(b,c,a) and (c,a,b)
from an equilateral triangle.

Explanation

Let A =(a,b,c),B=(b,c,a) and C =c,a,b)
` "Then" AB = sqrt((b-a)^2+(c-b)^2+(a-c)^2) `
`sqrt((a-b)^2+(b-c)^2+(c-a)^2)`
`"Similarly"BC = sqrt((a-b)^2+(b-c)^2+(c-a)^2) "and" CA =sqrt((a-b)^2+(b-c)^2+(c-a)^2)`
Thus AB=BC=CA
Hence `Delta ABC` is an equilateral triangle.(Proved)