If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \(2 x+4 y+5 z\) \(=8\) and \(3 x-2 y+3 z=5\) is \(\alpha x+\beta y+\gamma z+97=0\) then \(\alpha+\beta+\gamma=\)

[JEE Main 2023, 11 Apr (Shift 1)]

Question

If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \(2 x+4 y+5 z\) \(=8\) and \(3 x-2 y+3 z=5\) is \(\alpha x+\beta y+\gamma z+97=0\) then \(\alpha+\beta+\gamma=\)

[JEE Main 2023, 11 Apr (Shift 1)]

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