If $(p, q, r)$ is equidistant from $(1, 2, - 3), (2, - 3, 1)$ and $(- 3, 1, 2)$ , then $p + q + r$ $=$

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Solution

The correct option is C $0$
The given triangle is equilateral triangle as the distance between the vertices are equal.
As the triangle is equilateral, the centroid and the circumcentre are the same. The circumcentre is equidistant from the three vertices of a triangle.
The coordinates of the centroid are, $(\frac{1 + 2 - 3}{3}, \frac{2 - 3 + 1}{3}, \frac{2 + 1 - 3}{3})$
$= (0, 0, 0)$
Hence, the sum of the coordinates is $0$ .

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