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The equation of plane which passes through the point of intersection of lines $r ¯ = i^+ 2 j^+ 3 k^+ λ (3 i^+ j^+ 2 k^)$ and $r ¯ = 3 i^+ j^+ 2 k^+ μ (i^+ 2 j^+ 3 k^)$ where $λ, μ ∈ R$ and has the greatest distance from the origin is

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r ¯ . (7 i^+ 2 j^+ 4 k^) = 54

r ¯ . (5 i^+ 4 j^+ 3 k^) = 57

r ¯ . (3 i^+ 4 j^+ 5 k^) = 49

r ¯ . (4 i^+ 3 j^+ 5 k^) = 50

answer is D.

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Detailed Solution

For point of intersection

1 + 3 λ = 3 + μ 2 + λ = 1 + 2 μ 5 λ = 5 ⇒ λ = 1, μ = 1

Point of intersection (4,3,5)
For greatest distance from origin, perpendicular from origin meet at point of intersection
Hence equation

r ¯ (4 i^+ 3 j^+ 5 k^) = 50

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