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NDA 2017 Maths · Mathematics · Three Dimensional Geometry · medium

The plane through the point P(3,4,12) perpendicular to the line OP (O being the origin) is at a distance of what from the origin?

Single correct option

The plane through the point P(3,4,12)P(3,4,12) perpendicular to the line OPOP (OO being the origin) is at a distance of what from the origin?
  1. A. 169169
  2. B. 1212
  3. C. 55
  4. D. 1313
Show answer and solution

Answer: (D) 1313

The plane 3x+4y+12z=d3x+4y+12z=d passes through PP, so d=9+16+144=169d=9+16+144=169. The distance from OO is 1699+16+144=16913=13\frac{169}{\sqrt{9+16+144}}=\frac{169}{13}=13, which is just ∣OP∣|OP|. The value 169169 is dd without dividing by the normal length.
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Original question written in the NDA 2017 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