Question

If a line makes angles $\alpha ,\beta ,\gamma$ with coordinate axes, find
${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma +1$

Answer 1

If a line makes $\alpha ,\beta ,\gamma$ with the co-ordinates axes,

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

$\therefore {\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma -1=0$

Hence, the answer is $0$.