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NDA 2024 Maths · Mathematics · Three Dimensional Geometry · medium

If l,m,n are its direction cosines, then l+m+n equals

Single correct option

A line has direction ratios 1,2,21,2,2. If l,m,nl,m,n are its direction cosines, then l+m+nl+m+n equals
  1. A. 55
  2. B. 11
  3. C. 53\frac{5}{3}
  4. D. 59\frac{5}{9}
Show answer and solution

Answer: (C) 53\frac{5}{3}

The magnitude of the direction ratio vector is 1+4+4=3\sqrt{1+4+4}=3, so (l,m,n)=(13,23,23)(l,m,n)=\left(\frac13,\frac23,\frac23\right) and l+m+n=53l+m+n=\frac53. Trap: 55 is the sum of the ratios themselves, and 11 is the value of l2+m2+n2l^2+m^2+n^2, not of l+m+nl+m+n.
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