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NDA 2016 Maths · Mathematics · Three Dimensional Geometry · medium

For any line, the direction cosines l,m,n satisfy l^2+m^2+n^2=1. 2. The direction cosines of a line with direction ratios 2,-3,6 are 2/7,-3/7,6/7 (up…

Single correct option

Consider the following statements:
1. For any line, the direction cosines l,m,nl,m,n satisfy l2+m2+n2=1l^2+m^2+n^2=1.
2. The direction cosines of a line with direction ratios 2,−3,62,-3,6 are 27,−37,67\dfrac27,-\dfrac37,\dfrac67 (up to an overall sign).
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

Statement 1 is the basic identity of direction cosines and is true. For ratios 2,−3,62,-3,6 the norm is 4+9+36=7\sqrt{4+9+36}=7, so the direction cosines are ±(2/7,−3/7,6/7)\pm(2/7,-3/7,6/7), making statement 2 true as well.
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Original question written in the NDA 2016 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