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J & K CET Engineering J and K - CET Engineering Solved Paper-2013

  • question_answer
    The position vector of a point R which divides the line joining \[P(6,\,3,-2)\]and \[Q(3,1,-4)\]Q(3,1, - 4) in the ratio \[2:1\] externally is

    A)  \[\hat{i}+3\hat{j}-2\hat{k}\]     

    B)  \[3\hat{i}-\hat{k}\]

    C)  \[-\hat{j}-6\hat{k}\]         

    D)  \[2\hat{i}-\hat{j}\]

    Correct Answer: C

    Solution :

    Let position vector of P and Q are Day \[OP=6\hat{i}+3\hat{j}-2\hat{k}\] and \[OQ=3\hat{i}+\hat{j}-4\hat{k}\] Now, by section formula \[OR=\left[ \frac{2\times OQ-1\times OP}{2-1} \right]\] \[=\left( \frac{2(3\hat{i}+\hat{j}-4\hat{k})-(6\hat{i}+3\hat{j}-2\hat{k})}{1} \right)\] \[=\left\{ \frac{6\hat{i}+2\hat{j}-8\hat{k}-6\hat{i}-3\hat{j}+2\hat{k}}{1} \right\}\] \[=(\hat{j}\,\,-\,6\hat{k})\]


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