Let \(L\), be the line \(\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}\) and let \(S\) be the set of all points \((a, b, c)\…

Let \(L\), be the line \(\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}\) and let \(S\) be the set of all points \((a, b, c)\) on \(L\), whose distance from the line \(\frac{x+1}{2}=\frac{y+1}{3}=\frac{z−9}{0}\) along the line \(L\) is \(7\). Then \(\sum _{(a,\text{  }b,\text{  }c)\in S}(a+b+c)\) is equal

[JEE Main 2026, 22 Jan (Shift 2)]