For real numbers \(\alpha\) and \(\beta \neq 0\), if the point of intersection of the straight lines \(\frac{x-\alpha}{1…

For real numbers \(\alpha\) and \(\beta \neq 0\), if the point of intersection of the straight lines \(\frac{x-\alpha}{1}=\frac{y-1}{2}=\frac{z-1}{3}\) and \(\frac{x-4}{\beta}=\frac{y-6}{3}=\frac{z-7}{3}\) lies on the plane \(x+2 y-z=8\), then \(\alpha-\beta\) is equal to:

[JEE Main 2021, 27 Jul (Shift 2)]