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 - 2z = -2

• 2x - z = 2

• x - y - z = 0

• x + 3y + z = 4

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:

The equation of the required plane is given by

2x - y - 4 + λ(y + 2z - 4) = 0 ..................(i)

This plane passes through (1, 1, 0)

∴ 2(1) - 1 - 4 + λ(1 + 0 - 4) = 0

⇒ λ = -1

Substitution λ = -1 in (i), we get

2x - y - 4 - 1(y + 2z - 4) = 0

⇒ x - y - z = 0