a point moves such that the sum of the square of its distances from the six faces of acube is consta

Asked by  | 28th Dec, 2008, 05:07: PM

Expert Answer:

Let the coordinates of the cube be (a,0,0) , (-a,0,0) , (0,b,0) , (0,-b,0) , (0,0,c) , (0,0,-c)

Let the given point be P(x,y,z)

Given: Point P(x,y,z) moves such that the sum of the square of its distances from the six faces of acube is constant.

Hence, (x-a)2 + (x+a)2 + (y-b)2 + (y+b)2 + (z-c)2 + (z+c)2 = K, where K is a constant.

Solving this we get

x2 + y2 + z2 = K - a2 - b2 - c2 which is the equation of a sphere with centre (0,0,0) and radius K - a2 - b2 - c2

 

Answered by  | 3rd Jan, 2009, 12:49: PM

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