Question

A plane makes intercepts $a,b,c$ at $A,B,C$ on the coordinates axes, respectively. If the centroid of $∆ABC$ is at $(3,2,1)$, then the equation of the plane is

• A. $x+2y+3z=9$
• B. $2x–3y–6z=18$
• C. $2x+3y+6z=18$
• D. $2x+y+6z=18$
• E. $2x+3y+6z=9$

Answer 1

The correct option is C

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

Explanation for the correct option:

Step 1: Find the coordinates of $A,B,C$.

As $A,B,C$ are the intersection of planes.

So, Coordinates of $A,B,C$ will $(a,0,0),(0,b,0),(0,0,c)$.

Centroid of $∆ABC$ is $(3,2,1)$

So, $a=9,b=6$ and $c=3$.

Step 2: Find the equation of the plane:

Use the obtained points to get the equation of the plane.

$\begin{array}{rcl}\frac{x}{9}+\frac{y}{6}+\frac{z}{3}& =& 1\\ & \Rightarrow & 2x+3y+6z=18\end{array}$

Hence, option (C) is the correct answer.