If a point \(P(\alpha, \beta, \gamma)\) satisfying \((\alpha \beta \gamma)\left(\begin{array}{ccc}2 & 10 & 8 \\ …

If a point \(P(\alpha, \beta, \gamma)\) satisfying \((\alpha \beta \gamma)\left(\begin{array}{ccc}2 & 10 & 8 \\ 9 & 3 & 8 \\ 8 & 4 & 8\end{array}\right)=\left(\begin{array}{lll}0 & 0 & 0\end{array}\right)\) lies on the plane \(2 x+\) \(4 y+3 z=5\), then \(6 \alpha+9 \beta+7 \gamma\) is equal to:

[JEE Main 2023, 31 Jan (Shift 2)]