Point of intersection of two lines

Consider the following two lines, $L_1$ and $L_2$.

$L_1$ passes through the point $A_1(2, 3, 1)$ and has direction $\tvec{u} = \tvec{i} + 2\tvec{j} - \tvec{k}$.

$L_2$ passes through the point $A_2(1, 3, 2)$ and has direction $\tvec{v} = -\tvec{i} - \tvec{j} + \tvec{k}$.

Find the coordinates of the point of intersection of the two lines.