Given :

Equation of plane : 2x + 4y - z = 1

Equation of line :

To Find : Point of intersection of line and plane.

Let P(a, b, c) be point of intersection of plane and line.

As point P lies on the line, we can write,

⇒a = 2k+1, b = -3k+2, c = 4k-3 ………(1)

Also point P lies on the plane

2a + 4b – c = 1

⇒2(2k+1) + 4(-3k+2) – (4k-3) = 1 …..from (1)

⇒4k + 2 – 12k + 8 – 4k + 3 = 1

⇒-12k = -12

⇒k = 1

,

Therefore, co-ordinates of point of intersection of given line and plane are

P ≡