If a line makes an angle of frac{pi}{4} with | vedclass

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(B) Let the angles made by the line with the positive directions of the $x$,$y$,and $z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given $\alp

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$\frac{\pi}{2}$

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(B) Let the angles made by the line with the positive directions of the $x$,$y$,and $z$-axes be $\alpha$,$\beta$,and $\gamma$ respectively.Given $\alpha = \frac{\pi}{4}$ and $\beta = \frac{\pi}{4}$.The direction cosines of the line are $l = \cos \alpha$,$m = \cos \beta$,and $n = \cos \gamma$.We know that $l^2 + m^2 + n^2 = 1$.Substituting the values,we get $\cos^2(\frac{\pi}{4}) + \cos^2(\frac{\pi}{4}) + \cos^2 \gamma = 1$.Since $\cos(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}$,we have $(\frac{1}{\sqrt{2}})^2 + (\frac{1}{\sqrt{2}})^2 + \cos^2 \gamma = 1$.$\frac{1}{2} + \frac{1}{2} + \cos^2 \gamma = 1$.$1 + \cos^2 \gamma = 1$.$\cos^2 \gamma = 0$,which implies $\cos \gamma = 0$.Therefore,$\gamma = \frac{\pi}{2}$.

If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of the $x$-axis and $y$-axis,then the angle that the line makes with the positive direction of the $z$-axis is

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