PrepRung
Sign inSign up free

NDA 2022 Maths · Mathematics · Three Dimensional Geometry · medium

For any line in space, the sum of squares of its direction cosines is 1. 2. The direction ratios of the x-axis are uniquely (1,0,0).

Single correct option

Which of the following statements is/are correct?
1. For any line in space, the sum of squares of its direction cosines is 11.
2. The direction ratios of the xx-axis are uniquely (1,0,0)(1,0,0).
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

Statement 1 is true: l2+m2+n2=1l^2+m^2+n^2=1 always. Statement 2 is false: direction ratios are only proportional numbers, so (5,0,0)(5,0,0) or (−2,0,0)(-2,0,0) also represent the xx-axis; only the direction cosines (±1,0,0)(\pm1,0,0) are fixed up to sign. Hence 11 only.
Report a mistake

Original question written in the NDA 2022 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