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NDA 2023 Maths · Mathematics · Three Dimensional Geometry · hard

The equation of the plane which contains the x-axis and passes through the point (0,2,3) is

Single correct option

The equation of the plane which contains the xx-axis and passes through the point (0,2,3)(0,2,3) is
  1. A. 2y−3z=02y-3z=0
  2. B. 3y−2z=03y-2z=0
  3. C. 3y+2z=03y+2z=0
  4. D. 3y−2z=13y-2z=1
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Answer: (B) 3y−2z=03y-2z=0

A plane containing the xx-axis has the form by+cz=0by+cz=0 (no xx term and no constant). Putting (0,2,3)(0,2,3) gives 2b+3c=02b+3c=0, so (b,c)=(3,−2)(b,c)=(3,-2) and the plane is 3y−2z=03y-2z=0. The option 2y−3z=02y-3z=0 gives 4−9≠04-9\ne0.
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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