JEE Main 2024 Mathematics question
Let a line passing through the point (−1, 2, 3) intersect the lines L₁ : (x − 1)/3 = (y − 2)/2 = (z + 1)/(−2) at M(α, β, γ) and L₂ : (x + 2)/(−3) = (y − 2)/(−2) = (z − 1)/4 at N(a, b, c). Then the value of (α + β + γ)²/(a + b + c)² equals .
Answer: 196
Solution
M = (3λ + 1, 2λ + 2, −2λ − 1) and N = (−3t − 2, −2t + 2, 4t + 1). The direction ratios of the line through A(−1, 2, 3) are (3λ + 2, 2λ, −2λ − 4)
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