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

  • question_answer
    If the position vector of one end of the line segment AB be \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] and the position vector of its middle point be \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] then the position vector of the other end is

    A) \[4\mathbf{i}+3\mathbf{j}+5\mathbf{k}\]      

    B) \[4\mathbf{i}-3\mathbf{j}+7\mathbf{k}\]

    C) \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\]

    D) \[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\]

    Correct Answer: C

    Solution :

    \[\overrightarrow{OA}=2\mathbf{i}+3\mathbf{j}-\mathbf{k},\] \[\overrightarrow{OP}=3(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] \[\overrightarrow{OB}=?\] we have \[\overrightarrow{OP}=\frac{\overrightarrow{OA}+\overrightarrow{OB}}{2}\]                 \[\Rightarrow \overrightarrow{OB}=2\overrightarrow{OP}-\overrightarrow{OA}\]           \[=4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] Trick : By inspection, middle point of \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] and \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] is \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}).\]       


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