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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    The vectors\[\mathbf{c},\,\,\mathbf{a},\,\,=x\mathbf{i}+y\mathbf{j}+z\mathbf{k}\]and\[\mathbf{b}=\mathbf{j}\]are such that\[\mathbf{a},\,\,\mathbf{b},\,\,\mathbf{c}\]form a right handed system, then\[\mathbf{c}\]is

    A) \[0\]                                     

    B) \[y\,\,\mathbf{j}\]

    C) \[-z\,\,\mathbf{i}+x\,\,\mathbf{k}\]      

    D)        \[z\,\,\mathbf{i}-x\,\,\mathbf{k}\]

    Correct Answer: D

    Solution :

    Since,\[\mathbf{a,}\,\,\mathbf{b,}\,\,\mathbf{c}\]form a right handed system \[\therefore \]  \[\mathbf{c}=\mathbf{b}\times \mathbf{a}\]                 \[=\mathbf{j}\times (x\mathbf{i}+y\mathbf{j}+z\mathbf{k})\]                 \[=x(\mathbf{j}\times \mathbf{i})+z(\mathbf{j}\times \mathbf{k})\]                 \[=-x\mathbf{k}+z\mathbf{i}=z\mathbf{i}-x\mathbf{k}\]


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