Question

The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is ______.

Options

• x + 3y + z = 4

• 2x – z = 2

• x – 3y – 2z = –2

• x – y – z = 0

Answer 1

The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1, 1, 0) is x – y – z = 0.

Explanation:

(2x – y – 4) + λ(y + 2z – 4) = 0

Passes(1, 1, 0)

⇒ λ = –1

Plane(2x – y – 4) – (y + 2z – 4) = 0

x – y – z = 0