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Q.

If the origin is the centroid of the tetrahedron for which (2, –1, 3), (–1, 3, 1), (3, 4, –2) are three vertices then the fourth vertex is

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a

(4, 6, 2)

b

(4, –6, 2)

c

(–4, 6, –2)

d

(–4, –6, –2)

answer is B.

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Detailed Solution

If G is centroid of the tetrahedron formed by the vertices ABCD then G=A+B+C+D4

Hence, 

D=4G-A-B-C =-2+1-3,1-3-4,-3-1+2 =-4,-6,-2

 

 

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If the origin is the centroid of the tetrahedron for which (2, –1, 3), (–1, 3, 1), (3, 4, –2) are three vertices then the fourth vertex is