2. Solved Papers
  3. JEE Main & Advanced
  4. Physics
  5. Vectors

JEE Main & Advanced Physics Vectors JEE PYQ - Vectors

  • question_answer
    So, \[\left| \vec{B}-\vec{A} \right|=\left| {\vec{B}} \right|\Delta \theta =\left| {\vec{A}} \right|\Delta \theta \] 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 Online 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 :

    [a] 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 \[|\vec{C}|=\sqrt{\frac{4}{9}+\frac{1}{9}}=\sqrt{\frac{5}{9}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner