Answer:
Option B
Explanation:
Let \alpha,\beta and \gamma be the angles made by the line segment OP with X-axis, Y-axis and Z-axis , respectively
Given: \alpha=\frac{\pi}{4} and \beta=\frac{\pi}{3}
We know that \cos^{2}\alpha+\cos^{2}\beta+\cos^{2}\gamma=1
\therefore \cos^{2}\frac{\pi}{4}+\cos^{2}\frac{\pi}{3}+\cos^{2}\gamma=1
\Rightarrow \left(\frac{1}{\sqrt{2}}\right)^{2}+\left(\frac{1}{2}\right)^{2}+\cos^{2}\gamma=1
\Rightarrow \frac{1}{2}+\frac{1}{4}+\cos^{2}\gamma=1
\Rightarrow \cos^{2}\gamma=\frac{1}{4}
\Rightarrow \cos^{}\gamma=\frac{1}{\sqrt{2}}
\therefore \gamma=\frac{\pi}{4}
Hence , direction cosines are \cos\alpha,\cos\beta,\cos\gamma
i.e, \frac{1}{\sqrt{2}},\frac{1}{2},\frac{1}{\sqrt{2}}