Let $L_{1}and{L}_2$ be the following straight lines. $L_1:\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3}and{L}_2:\frac{x-1}{-3}=\frac{y}{-1}=\frac{z-1}{1}.$  Suppose the straight line $L:\text{}\frac{x-\alpha }{l}=\frac{y-1}{m}=\frac{z-\gamma }{-2}$ lies in the plane containing $L_{1}and{L}_2$ and passes through the point of intersection of $L_{1}and{L}_2.$ If the line $L$ bisects the acute angle between the lines $L_{1}and{L}_2,$ then