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 $$L_{2}: \frac{x-1}{-31} = \frac{y}{-1} = \frac{z-1}{1}$$.

Suppose the straight line

$$L: \frac{x - \alpha}{l} = \frac{y - 1}{m} = \frac{z - \gamma}{-2}$$

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 which of the following statements is/are TRUE?