Q101 / 160 · TS EAMCET 2020 (14 Sep Shift 2) · Mathematics

A plane meets the coordinate axes at $A, B, C$ respectively such that the centroid of the $\triangle A B C$ is $(2,3,5)$. Then, the equation of that plane is

  • A
    $3 x+3 y+3 z=10$
  • B
    $6 x+9 y+15 z=1$
  • C
    $2 x+3 y+5 z=1$
  • Correct answer
    D
    $15 x+10 y+6 z=90$

Solution

Let the equation of plane is, $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$ where $a, b, c$ are $x, y$ and $z$ intercepts $\therefore$ Centroid of $\triangle A B C$ is $\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)$. $\begin{array}{rlrl} \text { Given, }\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) & =(2,3,5) \\ \therefore \quad & a=6, b & =9, c=15 \end{array}$ Equation of plane is, $\frac{x}{6}+\frac{y}{9}+\frac{z}{15}=1$ $15 x+10 y+6 z=90$

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

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