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

  • question_answer
    The vectors \[\overrightarrow{AB}=3\mathbf{i}+4\mathbf{k},\] and \[\overrightarrow{AC}=5\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] are the sides of a triangle ABC. The length of the median through A is                                                                                                                [AIEEE 2003]

    A) \[\sqrt{18}\]          

    B) \[\sqrt{72}\]

    C) \[\sqrt{33}\]          

    D) \[\sqrt{288}\]

    Correct Answer: C

    Solution :

    P.V. of \[\overrightarrow{AD}=\frac{(3+5)i+(0-2)j+(4+4)k}{2}\]\[=4\mathbf{i}-\mathbf{j}+4\mathbf{k}\] \[|\overrightarrow{AD}|=\sqrt{16+16+1}=\sqrt{33}\].


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