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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 1

  • question_answer
    Given \[\left| {{{\vec{A}}}_{1}} \right|=2,\left| {{{\vec{A}}}_{2}} \right|=3\] and \[\left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|=3\]. The magnitude of \[\left( {{{\vec{A}}}_{1}}+2{{{\vec{A}}}_{2}} \right)\cdot \left( 3{{{\vec{A}}}_{1}}-4{{{\vec{A}}}_{2}} \right)\] is

    A) 64        

    B) 60                     

    C) 62                    

    D) 61

    Correct Answer: A

    Solution :

    [a] \[\left( {{{\vec{A}}}_{1}}+2{{{\vec{A}}}_{2}} \right)\,.\,\left( 3{{{\vec{A}}}_{1}}-4{{{\vec{a}}}_{2}} \right)\] \[3A_{1}^{2}-4{{\vec{A}}_{1}}{{\vec{A}}_{2}}+6{{\vec{A}}_{1}}{{\vec{A}}_{2}}-8A_{2}^{2}\] \[3A_{1}^{2}+2{{A}_{1}}{{A}_{2}}-8A_{2}^{2}\] \[3\times {{(2)}^{2}}-4-8-9\] \[12-4-72\] \[12-76=-64\] \[{{\left| {{{\vec{A}}}_{1}}+{{{\vec{A}}}_{2}} \right|}^{2}}={{\left( 3 \right)}^{2}}\] \[A_{1}^{2}+A_{2}^{2}+2{{\vec{A}}_{1}}{{\vec{A}}_{2}}=9\] \[4+9+\left( 2\times {{{\vec{A}}}_{1}}{{A}_{2}} \right)=9\] \[2{{\vec{A}}_{1}}{{\vec{A}}_{2}}=-4\]


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