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JEE Main & Advanced Physics Vectors Question Bank Multiplication of Vectors

  • question_answer
    A force \[\vec{F}=3\hat{i}+c\hat{j}+2\hat{k}\] acting on a particle causes a displacement \[\vec{S}=-4\hat{i}+2\hat{j}-3\hat{k}\] in its own direction. If the work done is 6J, then the value of c will be                 [DPMT 1997]

    A)                 12          

    B)                 6

    C)                 1             

    D)                 0

    Correct Answer: A

    Solution :

                        \[W=\overrightarrow{F}.\overrightarrow{s}=(3\hat{i}+c\hat{j}+2\hat{k}).(-4\hat{i}+2\hat{j}-3\hat{k})\]\[=-12+2c-6\]                                 Work done \[=6J\] (given)                                 \[\therefore \] \[-12+2c-6=6\]\[\Rightarrow \] \[c=12\]


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