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JEE Main & Advanced JEE Main Paper (Held On 16 April 2018)

  • question_answer
    Let\[\vec{A}=(\hat{i}+\hat{j})\]and\[\vec{B}=(\hat{i}-\hat{j}).\]The magnitude of a coplanar vector\[\vec{C}\]such that\[\vec{A}.\vec{C}=\vec{B}.\vec{C}=\vec{A}.\vec{B},\]  is given by [JEE Main 16-4-2018]

    A) \[\sqrt{\frac{5}{9}}\]                         

    B) \[\sqrt{\frac{10}{9}}\]

    C) \[\sqrt{\frac{20}{9}}\]                       

    D) \[\sqrt{\frac{9}{12}}\]    

    Correct Answer: A

    Solution :

     Let the vector                 \[\vec{C}\]be                 \[x\hat{i}+y\hat{j}\]                 \[\vec{A}.\vec{C}=x+y=1\]                 and \[\vec{B}.\vec{C}=2x-y=1\]                 Solving these two equations simultaneously                 \[x=2/3\]and \[y=1/3\]                 Hence \[|\vec{C}|=\sqrt{\frac{4}{9}+\frac{1}{9}}=\sqrt{\frac{5}{9}}\]


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