Question

Plane $ax+by+cz=1$ intersect axes in $A,B,C$ respectively. If $G(\frac{1}{6},-\frac{1}{3},1)$ is a centroid of $△ABC$ then $a+b+3c=$ _________.

• A. $\frac{4}{3}$
• B. $4$
• C. $2$
• D. $\frac{5}{6}$

Answer 1

The correct option is C $2$

let $A(\frac{1}{a},0,0)B(0,\frac{1}{b},0)C(0,0,\frac{1}{c})$
$centroid\Rightarrow (\frac{1}{3a},\frac{1}{3b},\frac{1}{3c})=(\frac{1}{6},\frac{-1}{3},1)$

On comparing we get,

$3a=6\Rightarrow a=23b=-3\Rightarrow b=-13c=1\Rightarrow c=\frac{1}{3}$
$\therefore a=2,b=-1,c=\frac{1}{3}$
$\therefore a+b+3c=2$
Only (C) is correct.