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Q.

In R3, consider the planes P1:y=0 and P2:x+z=1. Let P3 be a plane, different from P1 and P2, which passes through the intersection   P1 and P2. If the distance of the point (0,1,0) from P3 is 1 and the distance of a point (α,β,γ) from P3 is 2, then which of the following relations is (are) true?

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a

2α+β+2γ+2=0

b

2α-β+2γ+4=0

c

2α+β-2γ-10=0

d

2α-β+2γ-8=0

answer is B.

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Detailed Solution

Required plane be (x+z−1)+λy=0|λ−1|λ2+1+1=1⇒λ=−12P3:2x−y+2z−2=0distance of P3 from (α,β,γ) is 2|2α−β=2γ−2|4+1+4=22α−β+2γ−8=0, 2α−β+2γ+4=0
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