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NDA 2024 Maths · Mathematics · Three Dimensional Geometry · easy

The foot of the perpendicular drawn from the point (3,4,5) to the xy-plane is

Single correct option

The foot of the perpendicular drawn from the point (3,4,5)(3,4,5) to the xyxy-plane is
  1. A. (0,0,5)(0,0,5)
  2. B. (3,4,0)(3,4,0)
  3. C. (3,0,5)(3,0,5)
  4. D. (0,4,5)(0,4,5)
Show answer and solution

Answer: (B) (3,4,0)(3,4,0)

The xyxy-plane is z=0z=0. The perpendicular from a point to it is parallel to the zz-axis, so only the zz-coordinate changes, giving the foot (3,4,0)(3,4,0). Trap: (0,0,5)(0,0,5) is the foot on the zz-axis, and (3,0,5)(3,0,5), (0,4,5)(0,4,5) are the feet on the zxzx-plane and the yzyz-plane respectively.
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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