Let L1 : r = (î − ĵ + 2k̂) + λ (î − ĵ + 2k̂), λ ∈ R, L2 : r = (ĵ − k̂) + μ (3î + ĵ + pk̂), μ ∈ R, and L3 : r = δ(ℓ î + m ĵ + nk̂), δ ∈ R be three lines such that L1 is perpendicular to L2 and L3 is perpendicular to both L1 and L2. Then the point which lies on L3 is

Question

Accepted Answer

(1, −7, 4). The correct option is (1, −7, 4) because it satisfies the conditions of being on line L3, which is defined by the direction ratios derived from the perpendicular relationships between L1 and L2, ensuring that the point lies on the line defined by the scalar multiple of its direction vector.

Solution

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