Question

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $\Delta ABC$ is at $(3, 2, 1)$, then the equation of the plane is

• A. $x+2y+3z=9$
• B. $2x-3y-6z=18$
• C. $2x+3y+6z=18$
• D. $2x+y+6z=18$

Answer 1

Answer: (C)

$2x+3y+6z=18$

Answer 2

Coordinates of A, B and C are (a, 0, 0), (0, b, 0) and (0, 0, c) respectively Since, centroid of $\Delta ABC$ is (3, 2, 1).
$\therefore$ $\frac{a+0+0}{3}=3$
$\Rightarrow$ $a=9$ And $\frac{0+b+0}{3}=2$
$\Rightarrow$ $b=6$ And $\frac{0+0+c}{3}=1$
$\Rightarrow$ $c=3$
$\therefore$ Equation of required plane is $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$
$\Rightarrow$ $\frac{x}{9}+\frac{y}{6}+\frac{z}{3}=1$
$\Rightarrow$ $2x+3y+6z=18$