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, MN is perpendicular, i.e. parallel to the normal of the plane ∴
α
1
=
β−5
1
=
γ−5
1
=λ ⇒α=λ,β=λ+5,γ=λ−5 ∴λ+λ+5+λ+5=4 ⇒λ=−2 ∴N=(−2,3,5) Equation PN is