imo class 12 three dimensional geometry

The planes 2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 are:

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#IMO#Class 12#Mathematics#Three-Dimensional Geometry#logical-reasoning

The planes 2x + 3y + 4z = 5 and 4x + 6y + 8z = 12 are:

  • A. Parallel
  • B. Perpendicular
  • C. Intersecting at 45°
  • D. Coincident

Answer: A) Parallel

Explanation: Ratio of normals: 2/4 = 3/6 = 4/8 = 1/2. Since the normals are proportional, the planes are parallel.

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