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Question

Two systems of rectangular axes have the same origin. If a plane cuts them at distance a, b, c and a', b', c' from the origin, then

A
1a2+1b2+1c2+1a2+1b2+1c2=0
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B
1a2+1b21c2+1a2+1b21c2=0
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C
1a21b21c2+1a21b21c2=0
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D
1a2+1b2+1c21a21b21c2=0
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Solution

The correct option is D 1a2+1b2+1c21a21b21c2=0
Equation of planes be xa+yb+zc=1andxa+yb+zc=1 (Perpendicular distances of planes from origin is same)
∣ ∣ ∣11a2+1b2+1c2∣ ∣ ∣=∣ ∣ ∣11a2+1b2+1c2∣ ∣ ∣1a21a2=0.

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