The line \( l_{1} \) passes through the point \( (2, 6, 2) \) and is perpendicular to the plane \( 2x + y - 2z = 10 \). Then the shortest distance between the line \( l_{1} \) and the line \( \frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2} \) is:
\( 9 \)
\( \frac{13}{3} \)
\( \frac{19}{3} \)
\( 7 \)
