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

  • question_answer
    The figure formed by the four points \[\mathbf{i}+\mathbf{j}-\mathbf{k},\,\,\,2\mathbf{i}+3\mathbf{j},\] \[3\mathbf{i}+5\mathbf{j}-2\mathbf{k}\] and \[\mathbf{k}-\mathbf{j}\] is                                 [MP PET 2004]

    A) Rectangle              

    B) Parallelogram

    C) Trapezium             

    D) None of these

    Correct Answer: C

    Solution :

    Let \[A\equiv (1,\,1,-1),B\equiv (2,\,3,\,0),C\equiv (3,\,5,\,-2),\,D\equiv (0,\,-1,\,1)\] So, \[\overrightarrow{AB}=(1,\,2,\,1),\overrightarrow{BC}=(1,\,2,-2),\overrightarrow{CD}=(-3,-6,\,3),\overrightarrow{DA}=(1,\,2,\,-2)\] Clearly, \[\overrightarrow{BC}||\overrightarrow{DA},\]but \[AB\ne CD\]So, it is a trapezium.


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