Question

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.

Options

• 3x + 2y + z + 1 = 0

• 3x + 2y + z = 0

• 2x + 3y + z = 0

• x + y + z = 0

Answer 1

The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is 3x + 2y + z = 0.

Explanation:

The equation of the required plane is (x + 2y + 3z + 4) + λ(4x + 3y + 2z + 1) = 0 ....(i)

The plane passes through origin i. e., (0, 0, 0)

∴ 4 + λ = 0

⇒ λ = -4

Substituting value of λ in equation (i), we get

-15x - 10y - 5z = 0

⇒ 3x + 2y + z = 0