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NDA 2024 Maths · Mathematics · Three Dimensional Geometry · medium

The acute angle it makes with the x-axis is

Single correct option

A line has direction ratios 2,1,−22,1,-2. The acute angle it makes with the xx-axis is
  1. A. cos⁡−123\cos^{-1}\frac23
  2. B. cos⁡−113\cos^{-1}\frac13
  3. C. cos⁡−129\cos^{-1}\frac29
  4. D. sin⁡−123\sin^{-1}\frac23
Show answer and solution

Answer: (A) cos⁡−123\cos^{-1}\frac23

The magnitude of the direction ratios is 4+1+4=3\sqrt{4+1+4}=3, so the direction cosine with the xx-axis is 23\frac23 and the angle is cos⁡−123\cos^{-1}\frac23 (acute since cos⁡>0\cos>0). Trap: using 13\frac13 (the direction cosine for yy) or forgetting to divide by 3 gives the other options.
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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