Question

A line lies in $YZ-$plane and makes angle of ${30}^o$ with the $Y-$axis, then its inclination to the $Z-$axis is

• A. ${30}^o$ or ${60}^o$
• B. ${60}^o$ or ${90}^o$
• C. ${60}^o$ or ${120}^o$
• D. ${30}^o$ or ${150}^o$

Answer 1

Answer: (C)

${60}^o$ or ${120}^o$

since line lies on $y-z$ plane $\alpha ={90}^0$

$\beta ={30}^0$

$\therefore {\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$

$\therefore {\cos }^2{30}^0+{\cos }^2{30}^0+{\cos }^2\gamma =1$

${\cos }^2\gamma =\frac{1}{4}\Rightarrow \cos \gamma =\pm \frac{1}{2}$

$\gamma ={60}^0,{120}^0$

Ans: $C$