Question

If a line segment OP makes angles of \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) with the X-axis and Y-axis, respectively, then the direction cosines are

• A. \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
• B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
• C. \( \frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}} \)
• D. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)

Hint:

Direction cosines are determined by the cosine of the angles the line makes with the axes. The sum of the squares of the direction cosines should equal 1.

Answer 1

The Correct Option is D

Direction cosines of a line are calculated using the angles it makes with the coordinate axes. Here, the direction cosines corresponding to the given angles \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \) are computed.