Q101 / 160 · TS EAMCET 2019 (04 May Shift 2) · Mathematics

If a plane cuts the coordinate axes at $A, B$ and $C$ respectively such that the centroid of the triangle $A B C$ is $(6,6,3)$, then the equation of that plane.

  • A
    $x+y+z=18$
  • B
    $x+2 y+z=18$
  • Correct answer
    C
    $x+y+2 z=18$
  • D
    $2 x+y+z=18$

Solution

Let the equation of plane is $$ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 $$ Centroid of triangle formed by the coordinates axes at $(a, 0,0),(0, b, 0)$ and $(0,0, c)$ is $\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)$ Given $\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(6,6,3)$ $$ \therefore a=18, b=18, c=9 $$ Now, equation of plane is $$ \begin{aligned} & \frac{x}{18}+\frac{y}{18}+\frac{z}{9}=1 \\ & x+y+2 z=18 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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