Question

If a plane meets the co-ordinate axes in A,B,C such that the centroid of the triangle ABC is the point $(1,r,r^2),$ then equation of the plane is

• A. $x+ry+r^{2}z=3r^2$
• B. $r^{2}x+ry+z=3r^2$
• C. $x+ry+r^{2}z=3$
• D. $r^{2}x+ry+z=3$

Answer 1

The correct option is B $r^{2}x+ry+z=3r^2$

Let an equation of the required plane be $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$
This meets the coordinates axes in and A(a,0,0), B(0,b,0) and C(0,0,c).
So that the coordinates of the centroid of the triangle ABC are
$(\frac{a}{3},\frac{b}{3},\frac{c}{3})=(1,r,r^2)$ given $\Rightarrow a=3,b=3r,3r^2$ or $r^{2}x+ry+z=3r^2$