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 -

(1) x – 3y – 2z = – 2

(2) x – y – z = 0

(3) x + 3y + z = 4

(4) 2x – z = 2

Answer 1

Correct option (2) x – y – z = 0

Explanation:

Required equation of plane

(2x – y – 4) + λ (y + 2z – 4) = 0

Required plane passes through (1, 1, 0)

(2 – 1 – 4) + λ (1 + 0 – 4) = 0

λ = – 1

(2x – y – 4) – (y + 2z – 4) = 0

2x – 2y – 2z = 0

x – y – z = 0