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

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    The position vector of the points which divides internally in the ratio 2 : 3 the join of the points \[2\mathbf{a}-3\mathbf{b}\] and \[3\mathbf{a}-2\mathbf{b},\] is                                                                                          [AI CBSE 1985]

    A) \[\frac{12}{5}\mathbf{a}+\frac{13}{5}\mathbf{b}\]     

    B) \[\frac{12}{5}\mathbf{a}-\frac{13}{5}\mathbf{b}\]

    C) \[\frac{3}{5}\mathbf{a}-\frac{2}{5}\mathbf{b}\]           

    D) None of these

    Correct Answer: B

    Solution :

    Position vectors of the points which divides internally is, \[\frac{3(2\mathbf{a}-3\mathbf{b})+2(3\mathbf{a}-2\mathbf{b})}{5}=\frac{12\mathbf{a}-13\mathbf{b}}{5}.\]


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