$1.)$ Determine a function $r(t)$ for the line through the point $P(-3,4,2)$ that is perpendicular to both $u=($:$1,1,-5$:$)$ and $v=($:$0,1,1$:$).$ Express $r(t)$ in $($a$.)$ component form and $($b$.)$ in terms of $i,j,$ and $k.$