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NDA 2020 Maths · Mathematics · Three Dimensional Geometry · easy

The equation of the plane through the point (1,2,3) and perpendicular to the line with direction ratios 2,-1,4 is

Single correct option

The equation of the plane through the point (1,2,3)(1,2,3) and perpendicular to the line with direction ratios 2,−1,42,-1,4 is
  1. A. 2x−y+4z=02x-y+4z=0
  2. B. x+2y+3z=14x+2y+3z=14
  3. C. 2x−y+4z=122x-y+4z=12
  4. D. 2x−y+4z=82x-y+4z=8
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Answer: (C) 2x−y+4z=122x-y+4z=12

A plane perpendicular to a line has the direction ratios of the line as its normal, so the plane is 2(x−1)−(y−2)+4(z−3)=02(x-1)-(y-2)+4(z-3)=0, which expands to 2x−y+4z−12=02x-y+4z-12=0, so 2x−y+4z=122x-y+4z=12. The point (1,2,3)(1,2,3) satisfies it since 2−2+12=122-2+12=12. The option with 00 passes through the origin, and x+2y+3z=14x+2y+3z=14 uses the point's coordinates as the normal.
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Original question written in the NDA 2020 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