If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(X, Y\) and \(Z\)-axes…
If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(X, Y\) and \(Z\)-axes respectively, then the value of \(\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=\)
1
2
3
-1
Solution
Direction cosines will be \((\cos \alpha, \cos \beta, \cos \gamma)\)
So, \(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1\)
\(\Rightarrow \sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=2\)