The Locus of a point for which the sum of the squares of the distances from the coordinate axes is 16 units is

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x+y+z=4

x2+y2+z2=8

x2+y2+z2=16

x2+y2+z2=32

answer is B.

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Detailed Solution

Suppose that P(x,y,z) be any point on the locus. The perpendicular distance from P(x1,y1,z1) to the x− axis is y2+z2The perpendicular distance from P(x1,y1,z1) to the y− axis is x2+z2The perpendicular distance from P(x1,y1,z1) to the z− axis is x2+y2Hence, the sum of the squares of the distances from the point P(x1,y1,z1) to the coordinate axes is 2(x2+y2+z2)Therefore, the locus a point for which the sum of the squares of the distances from the coordinate axes is 16 units is x2+y2+z2=8

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