A) \[{{\sin }^{2}}\alpha +{{\cos }^{2}}\beta +{{\sin }^{2}}\gamma =1\]
B) \[{{\sin }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =1\]
C) \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\]
D) \[{{\cos }^{2}}\alpha +{{\sin }^{2}}\beta +{{\sin }^{2}}\gamma =1\]
Correct Answer: C
Solution :
Key Idea: If \[l,\,\,m,\,\,n\] be the direction cosines of a line, then\[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}=1\]. If \[\alpha ,\,\,\beta ,\,\,\gamma \] are the angles which the line makes with co-ordinate axes, then \[l=\cos \alpha ,\,\,m=\cos \beta ,\,\,n=\cos \gamma \] \[\therefore \]\[{{l}^{2}}+{{m}^{2}}+{{n}^{2}}={{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\]
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