JEE Main 2024 Mathematics question

Mathematics Three Dimensional Geometry JEE Main 2024

Let the line L intersect the lines x − 2 = −y = z − 1, 2(x + 1) = 2(y − 1) = z + 1 and be parallel to the line . Then which of the following points lies on L ?

(A)(−1/3, 1, 1)
(B)(−1/3, 1, −1)Correct
(C)(−1/3, −1, −1)
(D)(−1/3, −1, 1)

Answer: (B)

Solution

L₁: (x − 2)/1 = y/(−1) = (z − 1)/1 = λ and L₂: (x + 1)/(1/2) = (y − 1)/(1/2) = (z + 1)/1 = μ. Take M(2 + λ, −λ, 1 + λ) on L₁ and N(−1 + μ/2, 1 + μ/2, −1 + μ) on L₂. The direction ratios of MN must be

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Question ID VK-016535