Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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