A variable plane makes intercepts on and -axes and it makes a tetrahedron of volume 64 cu

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

Problem

A variable plane makes intercepts on

X, Y

and

Z

-axes and it makes a tetrahedron of volume 64 cu. u. The locus of foot of perpendicular from origin on this plane is (1)

(x^2 + y^2 + z^2)^3 = 384 xyz

(2)

xyz = 681

(3)

(x + y + z) \left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)^2 = 16

(4)

xyz(x + y + z) = 81