Let two vertices of triangle $A B C$ be $(2,4,6)$ and $(0,-2$, $-5)$, and its centroid be $(2,1,-1)$. If the image of third vertex in the plane $x+2 y+4 z=11$ is $(\alpha, \beta, \gamma)$, then $\alpha \beta+$ $\beta \gamma+\gamma \alpha$ is equal to [JEE Main 2023, 10 Apr (Shift 1)]

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Let two vertices of triangle \(A B C\) be \((2,4,6)\) and \((0,-2\), \(-5)\), and its centroid be \((2,1,-1)\). If the i…

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