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NDA 2018 Maths · Mathematics · Three Dimensional Geometry · hard

The line (x-2)/(1)=(y-1)/(2)=(z-3)/(2) meets the plane x+y+z=11 at the point

Single correct option

The line x−21=y−12=z−32\frac{x-2}{1}=\frac{y-1}{2}=\frac{z-3}{2} meets the plane x+y+z=11x+y+z=11 at the point
  1. A. (2,1,3)(2,1,3)
  2. B. (4,5,7)(4,5,7)
  3. C. (3,3,5)(3,3,5)
  4. D. (3,2,5)(3,2,5)
Show answer and solution

Answer: (C) (3,3,5)(3,3,5)

Put x=2+tx=2+t, y=1+2ty=1+2t, z=3+2tz=3+2t into the plane: 6+5t=116+5t=11, so t=1t=1 and the point is (3,3,5)(3,3,5). The point (2,1,3)(2,1,3) is the given point on the line, and it does not lie on the plane because 2+1+3=6≠112+1+3=6\ne11.
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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