Find the equation

r.(i - 2j + 3k) - 4 = 0

r.( - 2i + j + k) + 5 = 0

r.(i - 2j + 3k) + λ{r.( - 2i + j + k)} - 4 + 5λ = 0

⇒ r.[(1 - 2λ)i + ( - 2 + λ)j + (3 + λ)k] - 4 + 5λ = 0

⇒ (1 - 2λ)i + ( - 2 + λ)j + (3 + λ)k = - 5λ + 4

⇒

∴

⇒ 1 - 2λ = - 2 + λ

⇒ - 3λ = - 3

⇒ λ = 1

∴ Equation of the required plane

- x - y + 4z = - 1

X + y - 4z - 1 = 0

Vector equation of the required Plane

⇒ r.(i + j - 4k) - 1 = 0