JEE Main 2024 Mathematics question
Let Q and R be the feet of perpendiculars from the point P(a, a, a) on the lines x = y, z = 1 and x = −y, z = −1 respectively. If ∠QPR is a right angle, then 12a² is equal to .
Answer: 12
Solution
On the first line Q = (λ, λ, 1) and PQ·(1, 1, 0) = 0 gives (λ − a) + (λ − a) = 0, so λ = a and Q = (a, a, 1). On the second line R = (t, −t, −1) and
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