Let a unit vector \(\overrightarrow{O P}\) make an angle \(\alpha, \beta, \gamma\) with the positive directions of the c…

Let a unit vector \(\overrightarrow{O P}\) make an angle \(\alpha, \beta, \gamma\) with the positive directions of the co-ordinate axes \(O X, O Y, O Z\) respectively, where \(\beta \in\left(0, \frac{\pi}{2}\right)\) if \(\overrightarrow{O P}\) is perpendicular to the plane through points \((1,2,3),(2,3,4)\) and \((1,5,7)\), then which one of the following is true?

[JEE Main 2023, 30 Jan (Shift 1)]