A plane meets the coordinates axes at A, B and C such that centroid of $ΔABC$ is at the point (2, 3, 1). If the equation of the plane is $3x+2y +6z=k, $ then k is

3 18 1 0

18

The correct answer is Option (2) → 18 $3x+2y +6z=k$ $⇒\frac{x}{k/3}+\frac{y}{k/2}+\frac{z}{k/6}=1$ so $A(k/3,0,0),B(0,k/2,0),C(0,0,k/6)$ so centroid → $\left(\frac{k}{9},\frac{k}{6},\frac{k}{18}\right)=(2,3,1)$ so $k=18$