Question

A line makes angles $\alpha ,\beta ,\gamma$ with the co-ordinate axes. If $\alpha +\beta ={90}^{\circ }$, then $\gamma$ =

• A. $0$
• B. ${90}^{\circ }$
• C. ${180}^{\circ }$
• D. None of these

Answer 1

The correct option is B ${90}^{\circ }$

Here, $co{s}^2\alpha +co{s}^2(90-\alpha )+co{s}^2\gamma =1$
$\Rightarrow co{s}^2\alpha +si{n}^2\alpha +co{s}^2\gamma =1$
$\Rightarrow co{s}^2\gamma +1=1\Rightarrow \gamma ={90}^{\circ }$