Given: Equation of plane is 2x – 4y + z = 7

Line lies on the given plane.

Formula Used: Equation of a line is

Where (x₁, y₁, z₁) is a point on the line and b₁, b₂, b₃ : direction ratios of line.

Explanation:

Let

So the given line passes through the point (4, 2, k)

Since the line lies on the given plane, (4, 2, k) is a point on the plane.

Therefore, substituting the point on the equation for the plane,

⇒ 8 – 8 + k = 7

⇒ k = 7