JEE Main 2024 Mathematics question
Let the image of the point (1, 0, 7) in the line be the point (α, β, γ). Then which one of the following points lies on the line passing through (α, β, γ) and making angles and with y-axis and z-axis respectively and an acute angle with x-axis?
Answer: (A)
Solution
The foot of the perpendicular from A(1, 0, 7) to the line is M(K, 2K + 1, 3K + 2) with AM ⊥ (1, 2, 3): (K − 1) + 2(2K + 1) + 3(3K − 5) = 0, so K = 1 and M = (1, 3, 5). The image is A′ = (1, 6, 3). Direction cosines:
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