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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        If\[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=144\]and\[|\overrightarrow{a}|=4,\]Then\[|\overrightarrow{b}|\]is equal to

    A)  12                                         

    B)  3

    C)  8                                            

    D)  4

    Correct Answer: B

    Solution :

                    Key Idea: \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{b}.\overrightarrow{b}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\] Given \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=144\] and             \[|\overrightarrow{a}|=4\]                 \[|\overrightarrow{a}\times \overrightarrow{b}{{|}^{2}}+|\overrightarrow{a}.\overrightarrow{b}{{|}^{2}}=|\vec{a}{{|}^{2}}|\overrightarrow{b}{{|}^{2}}\] \[\Rightarrow \]               \[144=16.|\overrightarrow{b}{{|}^{2}}\] \[\Rightarrow \]               \[|\overrightarrow{b}{{|}^{2}}=9\] \[\Rightarrow \]               \[|\overrightarrow{b}|=3\]


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