Question

A line making angles ${45}^o$ and ${60}^o$ with the positive direction of $x-$ axis and $y-$ axis respectively. Then the angle made by the line with positive direction of $z-$ axis is

• A. ${60}^o$
• B. ${120}^o$
• C. ${60}^o$ or ${120}^o$
• D. $Noneofthese$

Answer 1

The correct option is C ${60}^o$ or ${120}^o$

$co{s}^2\alpha +co{s}^2\beta +co{s}^2\gamma =1$

$\alpha ={45}^{\circ }$

$\beta ={60}^{\circ }$

$\therefore co{s}^2{45}^{\circ }+co{s}^2{60}^{\circ }+co{s}^2\gamma =1$

$\frac{1}{2}+\frac{1}{4}+co{s}^2\gamma =1$

$co{s}^2\gamma =1-\frac{3}{4}$

$cos\gamma =\pm \frac{1}{2}$

$cos\gamma =\frac{1}{2},cos\gamma =-\frac{1}{2}$

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