Let a line passing through the point (4, 1, 0) intersect the line ${{\rm{L}}_1}:\frac{{x - 1}}{2} = \frac{{y - 2}}{3} = \frac{{z - 3}}{4}$ at the point $A(\alpha ,\beta ,\gamma )$ and the line ${{\rm{L}}_2}:x - 6 = y = - z + 4$ at the point $B(a,b,c)$. Then $\left| {\begin{array}{*{20}{l}} 1&0&1\\ \alpha &\beta &\gamma \\ a&b&c \end{array}} \right|$ is equal to