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JEE Main & Advanced Mathematics Vector Algebra Question Bank Critical Thinking

  • question_answer
    The vectors \[\overrightarrow{AB}=3\mathbf{i}+5\mathbf{j}+4\mathbf{k}\] and \[\overrightarrow{AC}=5\mathbf{i}-5\mathbf{j}+2\mathbf{k}\] are the sides of a triangle ABC. The length of the median through A is [UPSEAT 2004]

    A) \[\sqrt{13}\] unit

    B) \[\theta \] unit

    C) 5 unit

    D) 10 unit

    Correct Answer: C

    Solution :

    •                   
    • \[P.V.\]of \[\overrightarrow{AD}=\frac{(3+5)\mathbf{i}+(5-5)\mathbf{j}+(4+2)\mathbf{k}}{2}\]                                
    • \[\overrightarrow{AD}=\frac{8\mathbf{i}+6\mathbf{k}}{2}=4\mathbf{i}+3\mathbf{k}\]                   
    • \ Length of median \[=|\overrightarrow{AD}|=\sqrt{16+9}=5\] unit.


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