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NDA 2024 Maths · Mathematics · Three Dimensional Geometry · easy

The equation of the plane passing through (1,2,3) and having normal direction ratios 2,-1,4 is

Single correct option

The equation of the plane passing through (1,2,3)(1,2,3) and having normal direction ratios 2,−1,42,-1,4 is
  1. A. 2x−y+4z=142x-y+4z=14
  2. B. 2x−y+4z=62x-y+4z=6
  3. C. x+2y+3z=12x+2y+3z=12
  4. D. 2x−y+4z=122x-y+4z=12
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Answer: (D) 2x−y+4z=122x-y+4z=12

A plane with normal (2,−1,4)(2,-1,4) is 2x−y+4z=d2x-y+4z=d. Substituting the point, d=2−2+12=12d=2-2+12=12. Trap: sign errors in the middle term give 6 or 14, and swapping the point with the normal gives x+2y+3z=…x+2y+3z=\dots. Always substitute the point after fixing the normal.
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Original question written in the NDA 2024 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