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Question

# A variable plane forms a tetrahedron of constant volume 64 K3 with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is

A
x3+y3+z3=6K3
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B
xyz=6K3
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C
x2+y2+z2=4K2
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D
x2+y2+z2=4K2
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Solution

## The correct option is D xyz=6K3Let the variable plane forms the tetrahedron having the vertices (P,0,0),(0,Q,0),(0,0,R)Vertices of tetrahedron are (P,0,0),(0,Q,0),(0,0,R) and (0,0,0)Centroid of the tetrahedron is =(P4,Q4,R4)≡(h,k,j)Volume of tetrahedron =PQR6=64K3⇒P4.Q4.R4=6K3⇒h.k.j=6K3Therefore, locus of the centroid is xyz=6K3.

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