Let two vertices of a triangle ABC be (2,4,6) and ( 0,-2,-5 ), and its centroid be (2,1,-1). If the image of the third vertex in the plane x+2 y+4…

Let two vertices of a triangle ABC be $\displaystyle (2,4,6)$ and ( $\displaystyle 0,-2,-5$ ), and its centroid be $\displaystyle (2,1,-1)$. If the image of the third vertex in the plane $\displaystyle x+2 y+4 z=11$ is $\displaystyle (\alpha, \beta, \gamma)$, then $\displaystyle \alpha \beta+\beta \gamma+\gamma \alpha$ is equal to