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NDA 2023 Maths · Mathematics · Three Dimensional Geometry · medium

1/2,1/2,1/2 can be the direction cosines of a line. 2. Lines with direction ratios (1,2,3) and (3,0,-1) are perpendicular.

Single correct option

Consider the following statements:
1. 12,12,12\dfrac12,\dfrac12,\dfrac12 can be the direction cosines of a line.
2. Lines with direction ratios (1,2,3)(1,2,3) and (3,0,−1)(3,0,-1) are perpendicular.
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: (B) 2 only

Direction cosines must satisfy l2+m2+n2=1l^2+m^2+n^2=1, but 14+14+14=34\tfrac14+\tfrac14+\tfrac14=\tfrac34, so Statement 1 is false. For Statement 2, 1⋅3+2⋅0+3⋅(−1)=01\cdot3+2\cdot0+3\cdot(-1)=0, so the lines are perpendicular and the statement is true.
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Original question written in the NDA 2023 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