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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    Let \[\vec{a}\,-\,2\vec{b}\] and \[2\vec{a}\,-\vec{b}\] be position vectors of the points A and B respectively. The position vector of the point which divides AB in the ratio \[3:2\]externally is

    A)  \[\frac{8}{5}\,\vec{a}-\frac{7}{5}\vec{b}\]      

    B)  \[4\,\vec{a}+\vec{b}\]

    C)  \[\,\vec{a}+4\vec{b}\]

    D)  \[\frac{7}{5}\vec{b}-\frac{8}{5}\vec{a}\]

    Correct Answer: B

    Solution :

    Given,  \[A\,(\vec{a}-2\vec{b})\] and\[B\,\,(2\,\vec{a}-\vec{b})\]. The position vector of the point which divides AB in the ratio \[3:2\]externally is \[\frac{3(2\vec{a}-\vec{b})-(\vec{a}-2\vec{b})}{3-2}4\vec{a}+\vec{b}\]


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