NDA 2020 Maths · Mathematics · Three Dimensional Geometry · medium

A line can have direction cosines (1/2,1/2,1/2). 2. A line can have direction cosines ((1)/(√2),(1)/(√2),0).

Single correct option

Consider the following statements:
1. A line can have direction cosines

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

.
2. A line can have direction cosines

\left(\tfrac1{\sqrt2},\tfrac1{\sqrt2},0\right)

.
Which of the statements is/are correct?

Show answer and solution

Answer: (B) 2 only

Direction cosines must satisfy

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

. For statement 1 the sum is

\tfrac14+\tfrac14+\tfrac14=\tfrac34\ne1

, so it is impossible;

\left(\tfrac1{\sqrt3},\tfrac1{\sqrt3},\tfrac1{\sqrt3}\right)

would be the valid triple. For statement 2 the sum is

\tfrac12+\tfrac12+0=1

, so it is possible (a line in the xy-plane at

45^\circ

to both axes). Only statement 2 is correct.

Original question written in the NDA 2020 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