Question

If the plane 2x + y – 5z = 0 is rotated about its line of intersection with the plane 3x – y + 4z – 7 = 0 by an angle of π/2, then the plane after the rotation passes through the point : 

(A) (2, –2, 0) 

(B) (–2, 2, 0) 

(C) (1, 0, 2)

(D) (–1, 0, –2)

Answer 1

Correct option is (C) (1, 0, 2)

(2x + y – 5z) + λ(3x – y + 4z – 7) = 0 

Rotated by π/2 

(2 + 3λ)x + (1 – λ)y + (–5 + 4λ)z – 7λ = 0 

2x + y – 5z = 0 

2(2 + 3 λ) + (1 – λ) – 5(–5 + 4 λ) = 0 

⇒ 4 + 6 λ + 1 – λ + 25 – 20λ = 0

30 = 15λ

λ = 2

Required plane :- 8x – y + 3z – 14 = 0