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JEE Main & Advanced Physics Vectors Sample Paper Topic Test- Vectors

  • question_answer
    The resultant of \[\vec{A}\] and \[\vec{B}\] is \[{{\vec{R}}_{1}}\]. On reversing the vector \[\vec{B},\] the resultant becomes \[{{\vec{R}}_{2}}\]. What is the value of \[R_{1}^{2}\,+\,R_{2}^{2}\,?\]

    A) \[{{A}^{2}}+\,{{B}^{2}}\]

    B) \[{{A}^{2}}-{{B}^{2}}\]       

    C) \[2({{A}^{2}}+\,{{B}^{2}})\]

    D) \[2({{A}^{2}}-\,{{B}^{2}})\]

    Correct Answer: C

    Solution :

    [c] \[R_{1}^{2}\,=\,{{A}^{2}}+\,{{B}^{2}}+\,2\,AB\,\cos \theta \] \[R_{2}^{2}\,=\,{{A}^{2}}+\,{{B}^{2}}-\,2\,AB\,\cos \theta \] \[\therefore \]      \[R_{1}^{2}\,+\,R_{2}^{2}\,=2\,({{A}^{2}}+{{B}^{2}})\]


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