JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

  • question_answer
    The plane \[ax+by+cz=1\]meets the co-ordinate axes in A, B and C. The centroid of the triangle is [CET 1992]

    A)            \[(3a,3b,3c)\]

    B)            \[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\]

    C)            \[\left( \frac{3}{a},\frac{3}{b},\frac{3}{c} \right)\]

    D)            \[\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)\]

    Correct Answer: D

    Solution :

               Centroid is \[\left( \frac{\frac{1}{a}+0+0}{3},\frac{0+\frac{1}{b}+0}{3},\frac{0+0+\frac{1}{c}}{3} \right)\]            i.e.,\[\,\left( \frac{1}{3a},\frac{1}{3b},\frac{1}{3c} \right)\].


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