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Question -

Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.



Answer -

Given:
The points (1, 2, 3), (2, 3, 1) and (3, 1, 2)
An equilateral triangle is a triangle whose all sides are equal.
So let us prove AB = BC = AC
By using the formula,
The distance between any two points (a, b, c) and (m, n, o) is given by,

It is clear that,

AB = BC = AC

Δ ABC is a equilateral triangle

Hence Proved.

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