Question

If a plane meets the coordinate axes at $A, B$ and $C$ in such a way that the centroid of triangle $ABC$ is at the point $(1,2,3)$ then the equation of the plane is

• A. $\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=1$
• B. $\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$
• C. $\frac{x}{1}+\frac{y}{2}+\frac{z}{3}=\frac{1}{3}$
• D. $\frac{x}{1}-\frac{y}{2}+\frac{z}{3}=-1$

Answer 1

Answer: (B)

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

Answer 2

$(1,2,3)=\left(\frac{ a }{3}, \frac{ b }{3}, \frac{ c }{3}\right), a =3, b =6, c =9$