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Q:- A point moves so that the sum of the squares of its distances from the six faces of a cube given by x=±1, y=±1, z=±1 is 10 units . The locus of the point is

A. x^2+y^2+z^2=1

B. x^2+y^2+z^2=2

C. x+y+z =1

C. x+y+z=2

6 years ago


Answers : (1)


Dear Tapasranjan

planes are

x=±1, y=±1, z=±1

let the point is (x1,y1,z1)

 use distance formula of a point from a plane

(x1-1)2 +(x1+1)2 +(y1-1)2 +(y1+1)2 +(z1-1)2 +(z1+1)2 =10

2x12 + 2y12+ 2z1+ 6 =10

x12 + y12+ z1=2

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6 years ago

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