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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        If the vectors\[\overrightarrow{c},\overrightarrow{a}=x\hat{i}+y\hat{j}+z\hat{j}\]and\[\hat{b}=\hat{j}\]are such that \[\overrightarrow{a},\overrightarrow{c}\] and\[\overrightarrow{b}\]form a right handed system then\[\overrightarrow{c}\]is:

    A)  \[z\hat{j}-x\hat{k}\]                     

    B)  \[\overrightarrow{0}\]

    C)  \[y\hat{j}\]                                       

    D)  \[-z\hat{i}+x\hat{k}\]

    Correct Answer: A

    Solution :

                    Since,\[\overrightarrow{a},\text{ }\overrightarrow{c},\text{ }\overrightarrow{b}\] form a right handed system, therefore, \[\overrightarrow{c}\,\text{= }\overrightarrow{b}\times \overrightarrow{a}\] \[=\left| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    0 & 1 & 0  \\    x & y & z  \\ \end{matrix} \right|\] \[=z\hat{i}-x\hat{k}\]


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