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

  • question_answer
    Let \[\vec{a}\], \[\vec{b}\] and \[\vec{c}\] be the three vectors having magnitudes 1, 5 and 3, respectively, such that the angle between \[\vec{a}\] and \[\vec{b}\] is \[\theta \] and \[\vec{a}\times (\vec{a}\times \vec{b})=\vec{c}\]  Then tan \[\theta \] is equal to

    A) 0                     

    B) 2/3

    C) 3/5                   

    D) ¾

    Correct Answer: D

    Solution :

    [d] \[\vec{a}\times (\vec{a}\times \vec{b})=\vec{c}\Rightarrow \overrightarrow{\left| a \right|}\left| \vec{a}\times \vec{b} \right|=\overrightarrow{\left| c \right|}\] \[(\therefore \vec{a}\bot (\vec{a}\times \vec{b}))\] \[1(1\times 5)sin\theta =3\Rightarrow sin\theta =\frac{3}{5}\Rightarrow \tan \theta =\frac{3}{4}\]


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