JEE Main 2024 Mathematics question
The shortest distance between lines L₁ and L₂, where L₁ : (x − 1)/2 = (y + 1)/(−3) = (z + 4)/2 and L₂ is the line, passing through the points A(−4, 4, 3), B(−1, 6, 3) and perpendicular to the line (x − 3)/(−2) = y/3 = (z − 1)/1, is
Answer: (A)
Solution
L₂ passes through A(−4, 4, 3) and B(−1, 6, 3), with direction AB = (3, 2, 0) (and indeed (3, 2, 0)·(−2, 3, 1) = 0). L₁ has direction (2, −3, 2) and passes through (1, −1, −4). The cross product of
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