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
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
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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.
Updated On: Jan 12, 2026
- \( \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
- \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
- \( \frac{1}{2}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}} \)
- \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
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The Correct Option is D
Solution and Explanation
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.
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