A) \[\frac{\hat{A}\,\,\times \,\,\hat{B}}{AB\,\,\sin \,\,\theta }\]
B) \[\frac{\hat{A}\,\,\times \,\,\hat{B}}{AB\,\,\cos \,\,\theta }\]
C) \[\frac{\vec{A}\,\,\times \,\,\vec{B}}{AB\,\,\sin \,\,\theta }\]
D) \[\frac{\vec{A}\,\,\times \,\,\vec{B}}{AB\,\,\cos \,\,\theta }\]
Correct Answer: C
Solution :
Vector perpendicular to A and B, \[\vec{A}\,\,\times \,\,\vec{B}=AB\,\,\sin \,\,\theta \,\hat{n}\] \[\therefore \] Unit vector perpendicular to A and B \[\hat{n}=\frac{\vec{A}\,\,\times \,\,\vec{B}}{\left| {\vec{A}} \right|\,\,\times \left| {\vec{B}} \right|\,\sin \,\theta }\,\]
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