GATE AG 2010 • Q27 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The angle of intersection between the planes x − 3y + 2z = 10 and 2x + 4y + 5z = 0 is

Options:

  • (A) 30°
  • (B) 60°
  • (C) 75°
  • (D) 90°

Official Answer Key:

D

Step-by-Step Solution & Explanation

The angle between two planes equals the angle between their normal vectors: n₁=(1,−3,2), n₂=(2,4,5). n₁·n₂ = 1×2 + (−3)×4 + 2×5 = 2 − 12 + 10 = 0. Since the dot product is zero, the normals — and hence the planes — are perpendicular, 90°.

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