$(6$ points each$)$ Let $u=($:$1,1,0$:$)$ and $v=($:$-1,2,2$:$).$

$($a$)$ Compute $uv.$

$($b$)$ Compute the magnitude of $uv.$

$($c$)$ Find an equation of the plane normal to both $u$ and $v$ that passes through $P=(1,2,1).$