Q.

A variable plane intersects the coordinate axes at A,B,C and is at a constant distance 'p' from 0(0,0,0). Then the locus of the  centroid of the tetrahedron OABC is

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a

1x2+1y2+1z2=1p2

b

1x2+1y2+1z2=4p2

c

1x2 + 1y2 + 1z2 = 16p2

d

1x2 + 1y2 + 1z2 = 16 p2

answer is C.

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Detailed Solution

Intercepts of the plane = 4x, 4y, 4z where (x,y, z) is the centroid of the tetrahedron OABC.Here, 116x12 + 116y12 + 116z12 = 1p2
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A variable plane intersects the coordinate axes at A,B,C and is at a constant distance 'p' from 0(0,0,0). Then the locus of the  centroid of the tetrahedron OABC is