Reflection of the line x - 1 - 1 = y - 2 3 = z - 4 1 in the plane x + y + z = 7 is

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Given line x - 1 - 1 = y - 2 3 = z - 4 1 is passes through P ( 1 , 2 , 4 ) . To find the reflection of line we need one more point on the line clearly M ( 0 , 5 , 5 ) also lie on line. Let N ( α , β , γ ) be the reflection M in the x + y + z = 7 ∴   α 2 + β + 5 2 + γ + 5 2 = 7 ⇒   α + β + γ = 4 Also, M N is perpendicular, i.e. parallel to the normal of the plane ∴   α 1 = β - 5 1 = γ - 5 1 = λ ⇒   α = &