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Question

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 of P1 and P2. If the distance of the point (0, 1, 0) from
P3 is 2, then which of the following relation(s) is/are true?


A

2α+β+2γ+2=0

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B

2αβ+2γ+4=0

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C

2α+β2γ10=0

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D

2αβ+2γ8=0

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Solution

The correct option is D

2αβ+2γ8=0


Here, P3:(x+z1)+λy=0i.e. P3:x+λy+z1=0 ......(i)
whose distance from (0, 1, 0) is 1.
|0+λ+01|1+λ2+1=1 |λ1|=λ2+2 λ22λ+1=λ2+2λ=12 Equation ofP3 is 2xy+2z2=0. Distance from (α,β,γ) is 2. |2αβ+2γ2|4+1+4=2 2αβ+2γ2=±6 2αβ+2γ=8 and 2αβ+2γ=4


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