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

  • question_answer
    If a, b, c, d be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and \[\mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d},\] then quadrilateral ABCD is a

    A) Square   

    B) Rhombus

    C) Rectangle              

    D) Parallelogram

    Correct Answer: D

    Solution :

    Given \[\mathbf{a}+\mathbf{c}=\mathbf{b}+\mathbf{d}\Rightarrow \frac{1}{2}(\mathbf{a}+\mathbf{c})=\frac{1}{2}(\mathbf{b}+\mathbf{d})\] Here, mid points of \[\overrightarrow{AC}\] and \[\overrightarrow{BD}\] coincide, where \[\overrightarrow{AC}\] and \[\overrightarrow{BD}\] are diagonals. In addition, we know that diagonals of a parallelogram bisect each other. Hence quadrilateral is parallelogram.


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