Let a triangle \(PQR\) be such that \(P\) and \(Q\) lie on the line \(\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}\) and ar…

Let a triangle \(PQR\) be such that \(P\) and \(Q\) lie on the line \(\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}\) and are at a distance of \(6\) units from \(\mathrm{R}(1,2,3)\). If \((\alpha, \beta, \gamma)\) is the centroid of \(\triangle \mathrm{PQR}\), then \(\alpha+\beta+\gamma\) is equal to:

[JEE Main 2026, 5 Apr (Shift 2)]