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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2010

  • question_answer
    Let\[A(1,-1,2)\]and\[B(2,3,-1)\]be two points. If a point P divides AB internally in the ratio\[2:3,\]then the position vector of P is

    A)  \[\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+\hat{k})\]

    B)  \[\frac{1}{\sqrt{3}}(\hat{i}+6\hat{j}+\hat{k})\]

    C)  \[\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\]

    D)  \[\frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k})\]

    E)  \[\frac{1}{\sqrt{5}}(\hat{i}+\hat{j}+9\hat{k})\]

    Correct Answer: D

    Solution :

    The position vector of P \[=\frac{3A+2B}{3+2}\] \[=\frac{3(1,-1,2)+2(2,3,-1)}{5}\] \[=\frac{(7,3,4)}{5}\] \[=\frac{1}{5}(7\hat{i}+3\hat{j}+4\hat{k})\]


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