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NDA 2023 Maths · Mathematics · Three Dimensional Geometry · medium

The planes x+2y+2z=3 and 2x+y-2z=5 are

Single correct option

The planes x+2y+2z=3x+2y+2z=3 and 2x+y−2z=52x+y-2z=5 are
  1. A. parallel to each other
  2. B. inclined at 60∘60^\circ
  3. C. perpendicular to each other
  4. D. coincident
Show answer and solution

Answer: (C) perpendicular to each other

The normals are (1,2,2)(1,2,2) and (2,1,−2)(2,1,-2), with dot product 2+2−4=02+2-4=0. Hence the planes are perpendicular. They are not parallel because the normals are not proportional, and coincident planes would need proportional equations.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake