A) \[{{60}^{\text{o}}}\]
B) \[{{45}^{\text{o}}}\]
C) \[{{30}^{\text{o}}}\]
D) \[{{90}^{\text{o}}}\]
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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