JEE Advanced | 2015Set, Relation and FunctionHard
Question
In 
, 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 1 and the distance of a point (α, β, γ) from P3 is 2, then which of the following relations is (are) true ?
, 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 1 and the distance of a point (α, β, γ) from P3 is 2, then which of the following relations is (are) true ?Options
A.2α + β + 2γ + 2 = 0
B.2α − β + 2γ + 4 = 0
C.2α + β − 2γ − 10 = 0
D.2α − β + 2γ − 8 = 0
Solution
Let P3 : (x + z -1) + λy = 0
x + λy + z - 1 = 0 ...(i)
distance of (0,1,0) from P3 is 1
⇒
⇒ (λ - 1)2 = 2 + λ2
⇒ λ = -
∴ P3 is 2x - y + 2z - 2 = 0
distance from (α, β, γ) is
∴ 2α - β + 2γ - 2 = 6 or 2α - β + 2γ - 2 = - 6
2α - β + 2γ - 8 = 0 or 2α - β + 2γ + 4 = 0
x + λy + z - 1 = 0 ...(i)
distance of (0,1,0) from P3 is 1
⇒
⇒ (λ - 1)2 = 2 + λ2
⇒ λ = -
∴ P3 is 2x - y + 2z - 2 = 0
distance from (α, β, γ) is
∴ 2α - β + 2γ - 2 = 6 or 2α - β + 2γ - 2 = - 6
2α - β + 2γ - 8 = 0 or 2α - β + 2γ + 4 = 0
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