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Q.

The ortho centre of triangle formed by the points (2,1,5),(3,2,3), (4,0,4) is

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a

(3,1,4)

b

(4,0,4)

c

(2,1,5)

d

(3,2,3)

answer is D.

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Detailed Solution

AB=BC=CA=6ΔleABC is equilateral triangle

Since the triangle is equailateral triangle, all centers of equilateral triangle is coincident

Hence, the centroid of the triangle is Gx1+x2+x33,y1+y2+y33,z1+z2+z33

Hence the centroid is G2+3+43,1+23,5+3+43=G3,1,4

G=O=S=I=(3,1,4)

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