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NDA 2018 Maths · Mathematics · Three Dimensional Geometry · medium

The plane passing through (1,1,1) and perpendicular to the line with direction ratios 2,3,6 is

Single correct option

The plane passing through (1,1,1)(1,1,1) and perpendicular to the line with direction ratios 2,3,62,3,6 is
  1. A. 2x+3y+6z=112x+3y+6z=11
  2. B. x+y+z=11x+y+z=11
  3. C. 2x+3y+6z=62x+3y+6z=6
  4. D. 6x+3y+2z=116x+3y+2z=11
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Answer: (A) 2x+3y+6z=112x+3y+6z=11

A line's direction ratios serve as the normal of a perpendicular plane, so the plane is 2x+3y+6z=d2x+3y+6z=d. Through (1,1,1)(1,1,1): d=2+3+6=11d=2+3+6=11. The option with 6 is the constant for the intercept form, and the last option reverses the normal.
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Original question written in the NDA 2018 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