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Q.

If H,G,S,I are respectively orthocentre, centroid, circumcentre and incentre of a triangle formed by the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) then H + G + S + I =

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a

(6, 6, 6)

b

(8, 8, 8)

c

(4, 4, 4)

d

( 2, 2, 2)

answer is D.

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Detailed Solution

$\begin{array}{l} A (1, 2, 3), B (2, 3, 1), C (3, 1, 2) \\ \Rightarrow AB = BC = CA = \sqrt{6} \end{array}$
$∆ ABC$ is Equilateral triangle

$H = S = I = G = (\frac{1 + 2 + 3}{3}, \frac{2 + 3 + 1}{3}, \frac{3 + 1 + 2}{3}) = (2, 2, 2)$

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