Q.

Two systems of rectangular axes have the same origin.  If a plane cuts them at distances a, b, c and a1,b1,c1 from the origin, then

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a

1a2+1b2−1c2+1a12−1b12−1c12=0

b

1a2−1b2−1c2+1a12−1b12−1c12=0

c

1a2+1b2+1c2−1a12−1b12−1c12=0

d

1a2+1b2+1c2+1a12+1b12+1c12=0

answer is C.

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Detailed Solution

xa+yb+zc=1,xa1+yb1+zc1=1 Distance from (0,0,0)is same11a2+1b2+1c2=11(a|)2+1(b|)2+1(c|)2
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Two systems of rectangular axes have the same origin.  If a plane cuts them at distances a, b, c and a1,b1,c1 from the origin, then