Question

lf a line makes $\frac{\pi }{3},\frac{\pi }{4}$ with the $x$-axis, $y$-axis respectively, then the angle made by that line with the $z$- axis is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{5\pi }{12}$

Answer 1

Answer: (B)

$\frac{\pi }{3}$

We have, ${\left(\cos \left(\frac{\pi }{3}\right)\right)}^2+{\left(\cos \left(\frac{\pi }{4}\right)\right)}^2+\left(\cos \right(\gamma ){)}^2=1$
$\Rightarrow {\cos }^2\gamma =\frac{1}{4}$

$\Rightarrow \cos \gamma =\pm \frac{1}{2}$
$\Rightarrow \gamma =\frac{\pi }{3}$ or $\frac{2\pi }{3}$