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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2011

  • question_answer
    If a plane meets the coordinate axes at A, B and C, in such a way that the centroid of \[\Delta ABC\]is at the point (1, 2, 3), the equation of the plane is

    A)  \[\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1\]

    B)  \[\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\]

    C)  \[\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1/3\]

    D)  None of these

    Correct Answer: B

    Solution :

     Let the equation of the required plane be \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1.\]This meets the coordinate axes at A(a, 0, 0), B(0, b, 0) and C(0, 0, c). The coordinates of the controid of\[\Delta ABC\]are\[\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)\] \[\therefore \] \[\frac{a}{3}=1,\frac{b}{3}=2\] and          \[\frac{c}{3}=3\] \[\Rightarrow \] \[a=3,\text{ }b=6\]and\[c=a\] Hence, the equation of the plane is \[\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1\]


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