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BCECE Engineering BCECE Engineering Solved Paper-2009

  • question_answer
    If   the   vectors   \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\]  and =\[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\]are the sides of a \[\Delta ABC,\] then the length of the median through A is

    A) \[\sqrt{14}\]                      

    B)         \[\sqrt{18}\]     

    C)         \[\sqrt{29}\]     

    D)         4

    Correct Answer: B

    Solution :

    Position vector of median \[\overrightarrow{AD}=\frac{\overrightarrow{AB}+\overrightarrow{AC}}{2}\] \[=\frac{(-3+5)\hat{i}(0-2)\hat{j}+(4+4)\hat{k}}{2}\] \[=\hat{i}-\hat{j}+4\hat{k}\] \[\therefore \]\[|\overrightarrow{AD}|=\sqrt{{{1}^{2}}+{{(-1)}^{2}}+{{(4)}^{2}}}=\sqrt{18}\]


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