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JEE Main 2026 Mathematics question

MathematicsThree Dimensional GeometryJEE Main 2026

Let a line L₁ pass through the origin and be perpendicular to the lines L₂ : r⃗ = (3 + t)î + (2t − 1)ĵ + (2t + 4)k̂ and L₃ : r⃗ = (3 + 2s)î + (3 + 2s)ĵ + (2 + s)k̂, t, s ∈ ℝ. If (a, b, c), a ∈ ℤ, is the point on L₃ at a distance of √17 from the point of intersection of L₁ and L₂, then (a + b + c)² is equal to .

Answer: 4

Solution

L₂ and L₃ have directions (1,2,2) and (2,2,1); L₁ has direction (1,2,2)×(2,2,1)=(−2,3,−2). Intersecting L₁: λ(−2,3,−2) with L₂ gives t=−1, λ=−1,

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Question ID VK-015732