Prove that the triangle formed by joining the three points whose coordinates ere `(1,2,3),(2,3,1)a n d(3,1,2)` is an equilateral triangle.

Explanation

Three points are,`(1,2,3),(2,3,1)a n d(3,1,2)`

Then ,`PQ=[(1-2)^2+(2-3)^2+(3-1)^2)]^(1/2)`

`PQ=sqrt(6)`

`QR=[(2-3)^2+(3-1)^2+(1-2)^2)]^(1/2)`

`QR=sqrt(6)`

`PR=[(1-3)^2+(3-2)^2+(2-1)^2)]^(1/2)`

`PR=sqrt(6)`

As `PQ=QR=PR
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