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

  • question_answer
    A, B, C, D, E are five coplanar points, then \[\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}\] is equal to              [RPET 1999]

    A) \[\overrightarrow{DE}\]       

    B) \[3\,\overrightarrow{DE}\]

    C) \[2\,\overrightarrow{DE}\]  

    D) \[4\,\overrightarrow{ED}\]

    Correct Answer: B

    Solution :

    \[A,\,B,\,C,\,D,\,E\] are five co-planar points. \[\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}\] =\[(\overrightarrow{DA}+\overrightarrow{AE})+(\overrightarrow{DB}+\overrightarrow{BE})+(\overrightarrow{DC}+\overrightarrow{CE})\] = \[\overrightarrow{DE}+\overrightarrow{DE}+\overrightarrow{DE}\]=\[3\overrightarrow{DE}.\]            


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