Q101 / 160 · AP EAMCET 2018 (22 Apr Shift 1) · Mathematics

A plane cuts the coordinate axes $X, Y, Z$ at $A$, $B, C$ respectively such that the centroid of the $\triangle A B C$ is $(6,6,3)$. Then the equation of that plane is

  • A
    $x+y+z-6=0$
  • B
    $x+2 y+z-18=0$
  • C
    $2 x+y+z-18=0$
  • Correct answer
    D
    $x+y+2 z-18=0$

Solution

Let the equation of the plane is $$ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 $$ By the definition of the centroi $\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(6,6,3)$ Therefore, $$ \begin{aligned} a & =18 \\ b & =18 \\ c & =9 \end{aligned} $$ The equation of the plane becomes $$ \begin{array}{rlrl} & & \frac{x}{18}+\frac{y}{18}+\frac{z}{9} & =1 \Rightarrow \frac{x+y+2 z}{18}=1 \\ \Rightarrow \quad & x+y+2 z & =18 \\ \Rightarrow \quad x+y+2 z-18 & =0 \end{array} $$

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

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