JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    If \[\vec{a},\vec{b}\] are any two perpendicular vectors of equal magnitude and \[\left| 3\vec{a}+4\vec{b} \right|+\left| 4\vec{a}-3\vec{b} \right|=20\], then \[\left| {\vec{a}} \right|\] equals

    A)  10                               

    B)  5

    C)  2                                

    D)  1

    Correct Answer: C

    Solution :

    Let \[|\vec{a}|=|\vec{b}|=\lambda (>0)\,\] and \[\vec{a}.\vec{b}=0\] (Given) Now \[|3\vec{a}+4\vec{b}{{|}^{2}}\,=9{{\lambda }^{2}}\,+16{{\lambda }^{2}}\,=25{{\lambda }^{2}}\]   ?(1) And \[|4\vec{a}-3\vec{b}{{|}^{2}}\,=16{{\lambda }^{2}}\,+9{{\lambda }^{2}}\,=25{{\lambda }^{2}}\]     ?(2) \[\therefore \] From (1) and (2), we get \[|3\vec{a}+4\vec{b}|\,+|4\vec{a}-3\vec{b}|=5\lambda +5\lambda =20\] (Given) Hence \[\lambda =2\,=|\vec{a}|=|\vec{b}|\]

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