3d Geometry

Let the shortest distance between the lines


\(L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0\) and


\(L_{1}: x+1=y-1=4-z\) be \(2 \sqrt{6}\). If \((\alpha, \beta, \gamma)\) lies on \(L\),


then which of the following is NOT possible?