NDA 2025 Maths · Mathematics · Three Dimensional Geometry · medium

The direction cosines of a line can be (1/2,1/2,1/2). 2. The direction cosines l,m,n of a line satisfy l^2+m^2+n^2=1.

Single correct option

Consider the following statements:
1. The direction cosines of a line can be

\left(\tfrac12,\tfrac12,\tfrac12\right)

.
2. The direction cosines

l,m,n

of a line satisfy

l^2+m^2+n^2=1

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (B) $2$ only

Direction cosines always satisfy

l^2+m^2+n^2=1

, so statement 2 is correct. For

\left(\frac12,\frac12,\frac12\right)

the sum of squares is

\frac34\neq1

, so statement 1 is false. The equally inclined line has direction cosines

\pm\frac1{\sqrt3}

Original question written in the NDA 2025 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