Question

A triangular plane $ABC$ with centroid $(1,2,3)$ cuts the coordinates axes at $A,B,C$ respectively.

What is the equation of the plane $ABC$?

• A. $x+2y+3z=1$
• B. $3x+2y+z=3$
• C. $2x+3y+6z=18$
• D. $6x+3y+2z=18$

Answer 1

The correct option is D $6x+3y+2z=18$

$A=(x,0,0),B=(0,y,0),C=(0,0,z)$

Centroid of the triangle ABC = $(\frac{x+0+0}{3},\frac{0+y+0}{3},\frac{0+0+z}{3})$

Hence $(\frac{x}{3},\frac{y}{3},\frac{z}{3})=(1,2,3)$

$\therefore$ The intercepts made by the plane $ABC$ on the axes are $(x,y,z)=(3,6,9)$

Hence the equation of the plane $ABC$ is $\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$

$\Rightarrow 6x+3y+2z=18$