Question

A point moves so that the sum of the squares of its distances from the six faces of a cube given by $x=\pm 1,y\pm 1,z=\pm 1$ is 10 sq. units. Locus of the point is

• A. $x^2+y^2+z^2=1$
  
• B. x + y + z = 1
  
• C. $x^2+y^2+z^2=2$
  
• D. x + y + z = 2

Answer 1

The correct option is C $x^2+y^2+z^2=2$


Let point have coordinates P(x, y, z).
The six distances from given planes are
$|x\pm 1|,|y\pm 1|,|z\pm 1|.$ Hence,
$|x+1{|}^2+|x-1{|}^2+|y+1{|}^2+|y-1{|}^2+|z+1{|}^2+|z-1{|}^2=102x^2+2+2y^2+2+2z^2+2=10x^2+y^2+z^2=2$