NEET Sample Paper NEET Sample Test Paper-39

  • question_answer 4) \[\vec{A}\]and\[\vec{B}\]are two vectors and\[\theta \]is the angle between them, if\[\left| \vec{A}\times \vec{B} \right|=\sqrt{3}(\vec{A}.\vec{B})\] the value of \[\theta \]is:

    A)  \[\text{60 }\!\!{}^\circ\!\!\text{ }\]          

    B)  \[\text{45 }\!\!{}^\circ\!\!\text{ }\]

    C)  \[30{}^\circ \]

    D)  \[\text{90 }\!\!{}^\circ\!\!\text{ }\]

    Correct Answer: A

    Solution :

    \[\vec{A}\times \vec{B}=AB\sin \theta \]and \[\vec{A}.\vec{B}=AB\cos \theta .\] Given, \[|\vec{A}\times \vec{B}|=\sqrt{3}(\vec{A}.\vec{B})\] \[\Rightarrow \]\[AB\sin \theta =\sqrt{3}AB\cos \theta \] \[\Rightarrow \]\[\tan \theta =\sqrt{3}\] \[\theta ={{60}^{o}}\]

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