The equation of the plane, which makes with co-ordinate axes a triangle with its centroid $(\alpha , \beta , \gamma )$, is:

We know that  $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 ...\left(i\right)$

Centroid $\left(\frac{a}{3},\frac{b}{3},\frac{c}{3}\right)$

i.e. $\alpha =a/3,\beta =b/3,\gamma =c/3$

$\Rightarrow a=3\alpha ,b=3\beta ,c=3\gamma$

From equation $\text{ (i), }\frac{x}{3\alpha }+\frac{y}{3\beta }+\frac{z}{3\gamma }=1$

$\therefore \frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=3.$