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JEE Main & Advanced Physics Vectors Question Bank Topic Test - Vectors

  • question_answer
    If \[{{\bar{a}}_{1}}\] and \[{{\bar{a}}_{2}}\] are two non-collinear unit vectors and \[|{{\bar{a}}_{1}}+{{\bar{a}}_{2}}|=\sqrt{3},\] then the value of \[({{\bar{a}}_{1}}-{{\bar{a}}_{2}}).(2{{\bar{a}}_{1}}+{{\bar{a}}_{2}})\] is

    A) 2

    B) 3/2

    C) ½

    D) 1

    Correct Answer: C

    Solution :

    [c] \[\left| {{{\bar{a}}}_{1}}+{{{\bar{a}}}_{2}} \right|=\sqrt{a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos \theta }=\sqrt{3}\] \[\Rightarrow \]   \[\cos \theta =\frac{1}{2}\] \[({{\bar{a}}_{1}}-{{\bar{a}}_{2}})(2{{\bar{a}}_{1}}+{{\bar{a}}_{2}})=2a_{1}^{2}-a_{2}^{2}-{{a}_{1}}{{a}_{2}}\cos \theta =\frac{1}{2}\]


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