Question

If the plane 2 x + y - 5 z = 0 is rotated about its line of intersection with the plane 3 x - y + 4 z - 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

Answer: (C)

(1, 0, 2)

Answer 2

The correct answer is (C) : (1, 0, 2)
$P1: 2x +y - 52 = 0, P2: 3x - y + 4z-7=0$
Family of planes P1 and P2
$P: P1+λP2$
$∴ P: (2 + 3λ)x + (1 - λ)y+ (-5 + 4λ)z - 7λ=0$
$∵ P ⊥ P1 ∴ 4 + 6 λ +1 - λ + 25 - 20λ=0$
$λ = 2$
$P: 8x - y + 32 - 14 = 0$
It passes through the point $(1, 0, 2).$