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JEE Main & Advanced Mathematics Three Dimensional Geometry Question Bank Plane

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    The plane \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3\]meets the co-ordinate axes in \[A,B,C\]. The centroid of the triangle ABC is    [DCE 2005]

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

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

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

    D)            \[(a,b,c)\]

    Correct Answer: D

    Solution :

               Obviously, co-ordinates of A, B, C are respectively \[(3a,\,\,0,\,\,0),\] \[(0,\,\,3b,\,\,0)\] and \[(0,\,\,0,\,\,3c).\]            Hence centroid is \[(a,\,\,b,\,\,c).\]


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