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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Critical Thinking

  • question_answer
    If centroid of the tetrahedron \[OABC\], where \[A,B,C\]are given by (a, 2, 3),(1, b, 2) and (2, 1, c) respectively be (1, 2, -1), then distance of \[P(a,b,c)\] from origin is equal to

    A) \[\sqrt{107}\]

    B) \[\sqrt{14}\]

    C) \[\sqrt{107/14}\]

    D) None of these

    Correct Answer: A

    Solution :

    • Centroid\[\equiv \] \[\left( \frac{\sum x}{4},\,\frac{\sum y}{4},\frac{\sum z}{4}\, \right)\]= (1, 2, - 1)                   
    • \[\Rightarrow \,\,a=1,\,\,b=5,\,\,c=-9\]; \[\therefore \,\,\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}=\sqrt{107}\].


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