Consider the two lines given by

vec$(r{)}_1=($:$1,1,1$:$)+t($:$2,0,-1$:$)$

vec$(r{)}_2=($:$3,2,0$:$)+t($:$0,1,2$:$).$

$($a$)$ Find the vector vec$(n)=($:$2,0,-1$:$)($:$0,1,2$:$)$ that is perpendicular to both lines.

$($b$)$ Determine the distance between the two lines.