JEE Advanced 2015 Paper 1 Mathematics Q11

Mathematics

Problem

In R3\mathbb R^3, consider the planes P1:y=0P_1:y=0 and P2:x+z=1P_2:x+z=1. Let P3P_3 be a plane, different from P1P_1 and P2P_2, which passes through the intersection of P1P_1 and P2P_2. If the distance of the point (0,1,0)(0,1,0) from P3P_3 is 1 and the distance of a point (α,β,γ)(\alpha,\beta,\gamma) from P3P_3 is 2, then which of the following relations is (are) true?

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