Consider the points $P(1,2,1),Q(3,4,-2),$ and $R(-1,2,2).$

$($a$)[5$ points$]$ Find a unit vector perpendicular to vec$(PQ)$ and vec$(PR).$

$($b$)[3$ points$]$ Find the area of triangle $PQR.$

$($c$)[3$ points$]$ Find the equation of the plane which contains $P,Q,$ and $R.$

$($d$)$ Find the angle between vec$($PQ$)$ and vec$($ PR$),$points