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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    The perimeter of the triangle with vertices at \[(1,\,\,0,\,\,0),\,\,(0,\,\,1,\,\,0)\]and\[(0,\,\,0,\,\,1)\]is

    A) \[3\]                                     

    B) \[2\]

    C) \[2\sqrt{2}\]                      

    D)        \[3\sqrt{2}\]

    Correct Answer: D

    Solution :

    Let\[A=(1,\,\,0,\,\,0),\,\,B=(0,\,\,1,\,\,0)\]and\[C=(0,\,\,0,\,\,1)\] Now,     \[AB=\sqrt{{{(0-1)}^{2}}+{{(1-0)}^{2}}+{{0}^{2}}}=\sqrt{2}\]                 \[BC=\sqrt{{{(0-1)}^{2}}+{{(1-0)}^{2}}+{{0}^{2}}}=\sqrt{2}\] and        \[CA=\sqrt{{{(1-0)}^{2}}+{{0}^{2}}+{{(0-1)}^{2}}}=\sqrt{2}\] \[\therefore \]Perimeter of triangle\[=AB+BC+CA\]                 \[=\sqrt{2}+\sqrt{2}+\sqrt{2}\]                 \[=3\sqrt{2}\]


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