A variable plane at a distance of 1 unit from the origin cuts the coordinate axis at A,B and C . If the centroid (x,y,z) of triangle ABC satisfy the relation 1/x² + 1/y² + 1/z² = k, then the value of k is

A)3

B)1

C)1/3

D)9

let the plane be x/a + y/b + z/c = 1  with x,y,z intercepts as a, b, c respectively.

given perpendicular distance is 1, so

1/a² +1/b² + 1/c² = 1

centroid is (a/3, b/3, c/3)

so 9/a² +9/b² +9/c² = k   which implies k=9 on comparision

option D

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regards

Ramesh