JEE Main & Advanced Mathematics Vector Algebra Question Bank Mock Test - Vector Algebra

  • question_answer
    If the vectors \[\vec{a}\] and \[\vec{b}\] are linearly independent satisfying\[(\sqrt{3}tan\theta +1)\vec{a}+(\sqrt{3}sec\theta -2)\vec{b}\]=0, then the most general values of \[\theta \] are

    A) \[n\pi -\frac{\pi }{6},n\in z\]

    B) \[2n\pi \pm \frac{11\pi }{6},n\in z\]

    C) \[n\pi \pm \frac{\pi }{6},n\in z\]  

    D) \[2n\pi +\frac{11\pi }{6},n\in z\]

    Correct Answer: D

    Solution :

    [d] \[\sqrt{3}\tan \theta +1=0\] and \[\sqrt{3}\sec \theta -2=0\] \[\Rightarrow \theta =\frac{11\pi }{6}\] \[\Rightarrow \theta =2n\pi \pm \frac{11\pi }{6},n\in Z\]


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