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VIT Engineering VIT Engineering Solved Paper-2008

  • question_answer
    \[\vec{a}=\hat{i}-\hat{j}+\hat{k}\] and \[\vec{b}=2\hat{i}+4\hat{j}+3\hat{k}\] are one of the sides and medians respectively, of a triangle through the same vertex, then area of the triangle is

    A)  \[\frac{1}{2}\sqrt{83}\]

    B)  \[\sqrt{83}\]

    C)  \[\frac{1}{2}\sqrt{85}\]

    D)  \[\sqrt{86}\]

    Correct Answer: D

    Solution :

    Area of triangle \[\left\| \begin{matrix}    {\hat{i}} & {\hat{j}} & {\hat{k}}  \\    1 & -1 & 1  \\    2 & 4 & 3  \\ \end{matrix} \right\|\] \[=\left| -7\hat{i}-\hat{j}+6\hat{k} \right|=\sqrt{49+1+36}\] \[=\sqrt{86}\]


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