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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    If  \[\hat{a},\hat{b}\]  and  \[\hat{c}\]  are unit vectors satisfying \[\hat{a}-\sqrt{3}\hat{b}+\hat{c}=\vec{0}\], then the angle between the vectors \[\hat{a}\] and \[\hat{c}\] is

    A)  \[\frac{\pi }{6}\]                                             

    B)  \[\frac{\pi }{4}\]

    C)  \[\frac{\pi }{3}\]                                             

    D)  \[\frac{\pi }{2}\]

    Correct Answer: C

    Solution :

    \[|\widehat{a}+\widehat{c}{{|}^{2}}=|\sqrt{3}\widehat{b}{{|}^{2}}\Rightarrow 1+1+2\cos \theta =3\],                 Where \[\theta =\]angle between\[\widehat{a}\]and\[\widehat{c}\], \[\Rightarrow \cos \theta =\frac{1}{2}\].               So,\[\theta =\frac{\pi }{3}\]


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