Given :

Equation of plane : 2x + y + z = 7

Points :

A = (3, -4, -5)

B = (2, -3, 1)

To Find : Point of intersection of line and plane.

Formula :

Equation of line passing through A = (x₁, y₁, z₁) &

B = (x₂, y₂, z₂) is

Equation of line passing through A = (3, -4, -5) & B = (2, -3, 1) is

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

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

⇒a = k+3, b = -k - 4, c = -6k-5 ………(1)

Also point P lies on the plane

2a + b + c = 7

⇒2(k+3) + (-k-4) + (-6k-5) = 7 …..from (1)

⇒2k + 6 – k - 4 – 6k - 5 = 7

⇒-5k = 10

⇒k = -2

,

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

P ≡