A) \[{{60}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{30}^{o}}\]
D) \[{{90}^{o}}\]
Correct Answer: A
Solution :
| Key Idea: \[\vec{A}\times \vec{B}=AB\sin \theta \] and \[\vec{A}\,\,\centerdot \,\,\vec{B}=AB\cos \theta .\] |
| Given, \[\left| \vec{A}\times \vec{B} \right|=\sqrt{3}\,(\vec{A}\,\centerdot \,\,\vec{B})\] |
| \[\Rightarrow \] \[AB\sin \theta =\sqrt{3}\,AB\cos \theta \] |
| \[\Rightarrow \] \[\tan \theta =\sqrt{3}\] |
| \[\therefore \] \[\theta ={{60}^{o}}\] |
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