Answer :

Given: Points are A(a, b, c), B(b, c, a) and C(c, a, b)


To prove: the triangle formed by given points is an equilateral triangle


An equilateral triangle is a triangle whose all sides are equal


So we need to prove AB = BC = AC


Formula used:


The distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


The distance between A(a, b, c) and B(b, c, a) is AB,





The distance between B(b, c, a) and C(c, a, b) is AB,





The distance between A(a, b, c) and C(c, a, b) is AB,





Clearly,


AB = BC = AC


Thus, Δ ABC is a equilateral triangle


Hence Proved


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