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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) |
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Answer» 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 |
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