Let α , β , γ be mirror image of the point 2 , 3 , 5 in the line x − 1 2 = y − 2 3 = z − 3 4 . Then 2 α + 3 β + 4 γ is equal to

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Given: x - 1 2 = y - 2 3 = z - 3 4 Let, P ≡ 2 , 3 , 5 and R ≡ α , β , γ . Now, direction ratio of P R = α - 2 , β - 3 , γ - 5 And the line x - 1 2 = y - 2 3 = z - 3 4 will be perpendicular, So, using perpendicular condition we get, ⇒ α - 2 × 2 + β - 3 × 3 + γ - 5 × 4 = 0 ⇒ 2 α - 4 + 3 β - 9 + 4 γ - 20 = 0 ⇒ 2 α + 3 β + 4 γ = 33

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