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Question

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

A

$x+2y+3z=9$

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B

$2x–3y–6z=18$

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C

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

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D

$2x+y+6z=18$

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E

$2x+3y+6z=9$

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Solution

## 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 $\left(a,0,0\right),\left(0,b,0\right),\left(0,0,c\right)$.Centroid of $∆ABC$ is $\left(3,2,1\right)$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.$\begin{array}{rcl}\frac{x}{9}+\frac{y}{6}+\frac{z}{3}& =& 1\\ & ⇒& 2x+3y+6z=18\end{array}$Hence, option (C) is the correct answer.

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