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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        The vector\[\hat{i}+x\hat{j}+3\hat{k}\]is rotated through an angle\[\theta \]and doubled in magnitude, then it becomes\[4\hat{i}+(4x-2)\hat{i}+2\hat{k}\]. The value of\[x\] is:

    A)  \[\left( -\frac{2}{3},2 \right)\]                   

    B)  \[\left( \frac{1}{3},2 \right)\]

    C)  \[\left( \frac{2}{3},0 \right)\]                    

    D)  \[(2,7)\]

    Correct Answer: A

    Solution :

                    We have\[2|\hat{i}+x\hat{j}+3\hat{k}|\] \[=|4\hat{i}+(4x-2)\hat{j}+2\hat{k}|\] \[\Rightarrow \]               \[4({{x}^{2}}+10)=20+{{(4x-2)}^{2}}\] \[\Rightarrow \]               \[3{{x}^{2}}-4x-4=0\] \[\Rightarrow \]               \[x=2,-\frac{2}{3}\]


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