A plane meets the co-ordinates axes in A, B, C such that the centroid of triangle ABC is (a, b, c). The equation of the plane is :

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$

The plane meets the co−ordinate axes at A, B, C such that centroid of the triangle ABC is (a, b, c)

so, the plane cuts X−axis at (3 a, 0, 0)

So, X−intercept = 3 a

The plane cuts Y−axis at (0, 3 b, 0)

⇒ Y−intercept = 3 b

the plane cuts Z−axis at (0, 0, 3 c)

⇒ Z−intercept = 3 c

Therefore required equation is $\frac{x}{3 a}+\frac{y}{3 b}+\frac{z}{3 c}=1$

$\Rightarrow \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$