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The equation of a plane through the intersection of π₁ = 0 and π₂ = 0 has the form
Aπ₁ · π₂ = 0
Bπ₁ + λπ₂ = 0
Cπ₁ × π₂ = 0
D(π₁ - π₂) · λ = 0
Answer & Solution
Correct answer: B. π₁ + λπ₂ = 0
1. Let π₁ and π₂ be linear expressions in x, y, z each equal to zero on its plane.
2. Their linear combination π₁ + λπ₂ vanishes at any common point of the two planes.
3. Varying λ traces the pencil of planes through the intersection line.
4. So the family is π₁ + λπ₂ = 0.
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.6.5_
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