A variable plane at a distance of unit from the origin cuts the axes at ,

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A variable plane at a distance of

1

unit from the origin cuts the axes at

a

b

, and

c

. If the centroid

D(x,y,z)

\triangle ABC

satisfies the relation

\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=k

, then the value of

k

is (1) 3 (2) 1 (3)

\frac{1}{3}

(4) 9