JEE Main 2024 Mathematics question
A line with direction ratios 2, 1, 2 meets the lines x = y + 2 = z and x + 2 = 2y = 2z respectively at the points P and Q. If the length of the perpendicular from the point (1, 2, 12) to the line PQ is l, then l² is .
Answer: 65
Solution
Take P(λ, λ − 2, λ) and Q(μ − 2, μ/2, μ/2). The direction PQ ∥ (2, 1, 2) gives μ = 4 and λ = 6, so P = (6, 4, 6) and Q = (2, 2, 2). The line PQ is (x − 2)/2 = (y − 2)/1 = (z − 2)/2 = K.
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