A) \[\Delta \] is independent of \[\theta \]
B) \[\Delta \] is independent of \[\phi \]
C) \[\Delta \] is a constant
D) none of these
Correct Answer: B
Solution :
| \[\Delta =\left| \begin{matrix} \sin \theta \cos \phi & \sin \theta \sin \phi & \cos \theta \\ \cos \theta \cos \phi & \cos \theta \sin \phi & -\sin \theta \\ -\sin \theta \sin \phi & \sin \theta \cos \phi & 0 \\ \end{matrix} \right|\] |
| \[\Delta ={{\sin }^{2}}\theta \cos \theta \left| \begin{matrix} \cos \phi & \sin \phi & \cot \theta \\ \cos \phi & \sin \phi & -\tan \theta \\ -\sin \phi & \cos \phi & 0 \\ \end{matrix} \right|\] |
| \[\Delta =\sin \theta \] |
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