Question

A plane meets the axes in $A,B$ and $C$ such that centroid of the $△ABC$ is $(1,2,3)$. The equation of the plane is

• A. $x+\frac{y}{2}+\frac{z}{3}=1$
• B. $\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$
• C. $x+2y+3z=1$
• D. None of these

Answer 1

Answer: (B)

$\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$

Let the plane meets the coordinate axes at $A,B$ and $C$.
Let $OA=a,OB=b$ and $OC=c$
Then, the centroid of $△ABC$
is $(\frac{a}{3},\frac{b}{3},\frac{c}{3})=(1,2,3)$ ........ (given)
$\Rightarrow a=3,b=6,c=9$
Then, the equation of plane meet the coordinates axes is
$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$
i.e., $\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$