JEE Main 2024 Mathematics question
If the shortest distance between the lines L₁ : = (2 + λ)î + (1 − 3λ)ĵ + (3 + 4λ)k̂, λ ∈ R, L₂ : = 2(1 + μ)î + 3(1 + μ)ĵ + (5 + μ)k̂, μ ∈ R is , where gcd(m, n) = 1, then the value of m + n equals.
Answer: (B)
Solution
L₁: (2, 1, 3) + λ(1, −3, 4); L₂: (2, 3, 5) + μ(2, 3, 1). d₁ × d₂ = (−15, 7, 9) with |d₁ × d₂|² = 355, and
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