If a line makes an angle of $\pi / 4$ with the positive directions of each of $x$-axis and $y$-axis,

Question

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

Professor PC Thomas Classes · Answer

(b) : Let required angle is $	heta$\ $\because \quad l=\cos \frac{\pi}{4}, m=\cos \frac{\pi}{4}$, then $n=\cos 	heta$\ We know that $l^{2}+m^{2}+n^{2}=1$\ $\Rightarrow \quad \cos ^{2} \frac{\pi}{4}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} 	heta=1$\ $\Rightarrow \quad \frac{1}{2}+\frac{1}{2}+\cos ^{2} 	heta=1 \Rightarrow \cos ^{2} 	heta=0 \Rightarrow 	heta=\pi / 2$.\ Thus required angle is $\pi / 2$.\