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JEE Main & Advanced Mathematics Vector Algebra Question Bank Modulus of vector Algebra of vectors

  • question_answer
    ABCDE is a pentagon. Forces \[\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}\] act at a point. Which force should be added to this system to make the resultant \[{{\cos }^{-1}}\frac{4}{5}\]                                                                                                            [MNR 1984]

    A) \[\overrightarrow{AC}\]       

    B) \[\overrightarrow{AD}\]

    C) \[\overrightarrow{BC}\]       

    D) \[\overrightarrow{BD}\]

    Correct Answer: C

    Solution :

    \[\overrightarrow{AE}+\overrightarrow{ED}+\overrightarrow{DC}+\overrightarrow{AB}=\overrightarrow{AD}+\overrightarrow{DC}+\overrightarrow{AB}\]\[=\overrightarrow{AC}+\overrightarrow{AB}.\] Obviously, if \[\overrightarrow{BC}\] is added to this system, then it will be \[\overrightarrow{AC}+\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}+\overrightarrow{AC}=2\overrightarrow{AC}.\]


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