Q.

P is a point such that the sum of the squares of its distances from the planes x+y+z=0,  x+y−2z=0,x−y=0 is 5 then the locus of  P is

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a

x2+y2+z2=10

b

x2+y2+z2=25

c

x2+y2+z2=5

d

x2+y2+z2=50

answer is C.

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Detailed Solution

x1+y1+z132+x1+y1−2z162+x1−y122=5⇒x2+y2+z2=5
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P is a point such that the sum of the squares of its distances from the planes x+y+z=0,  x+y−2z=0,x−y=0 is 5 then the locus of  P is