AP EAMCET · Maths · Three Dimensional Geometry
If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of \(X, Y\) and \(Z\)-axes respectively, then the value of \(\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=\)
- A 1
- B 2
- C 3
- D -1
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Direction cosines will be \((\cos \alpha, \cos \beta, \cos \gamma)\) So, \(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1\) \(\Rightarrow \sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=2\)
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