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If $H, G, S, I$ are respectively orthocenter, centroid, circumcenter 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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$(6, 6, 6)$

$(2, 2, 2)$

$(4, 4, 4)$

$(8, 8, 8)$

answer is D.

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Detailed Solution

$A B = B C = C A = \sqrt{6} ∴ Δ A B C i s a n e q u i l a t e r a l T r i a n g l e . ∴ H = G = S = I H + G + S + I = 4 G = (8, 8, 8)$

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