Question

If a line makes angles ${90}^o,{60}^0$ and $\theta$ with $x,y$ and $z-$ axis respectively, where $\theta$ is acute, then find $\theta$.

Answer 1

if $\alpha$, $\beta$ and $\gamma$ are the angles made by the line with the $x,y$ and $z$ axes respectively, then ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$.

Therefore ${\cos }^{2}90°+{\cos }^{2}60°+{\cos }^2\theta =1\Rightarrow \cos \theta =\frac{\sqrt{3}}{2}\Rightarrow \theta =30°$