Which of the following represents the direction cosines of the line?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 2 Official Paper

Answer 1

Explanation:

If the direction cosine of the line is l, m, n, then l² + m² + n² = 1

For option (1):

\((0)^{2}+\left ( \frac{1}{2} \right )^{2}+\left ( \frac{1}{2} \right )^{2}=\frac{1}{4}+\frac{1}{4}\)

= \(\frac{1}{2}\neq 1\)

For option (2):

\(\left (\frac{1}{3} \right )^{2}+\left (\frac{1}{3} \right )^{2}+\left (\frac{1}{3} \right )^{2}=\frac{1}{9}+\frac{1}{9}+\frac{1}{9}\)

= \(\frac{1}{3}\neq 1\)

For option (3):

\((0)^{2}+\left ( \frac{1}{\sqrt{3}} \right )^{2}+\left ( \frac{1}{3} \right )^{2}=\frac{1}{3}+\frac{1}{9}\)

= \(\frac{4}{9}\neq 1\)

For option (4):

\(0^{2}+\left ( \frac{\sqrt{3}}{2} \right )^{2}+\left ( \frac{1}{2} \right )^{2}=1\)

Hence, the correct answer from the given option is (4)

0, \(\frac{\sqrt{3}}{2}, \frac{1}{2}\)