$2.$ Consider the plane x $$ y $+$ z $=3$ and the straight line with equation r$($t$)=$ ht $+2,1$ t$,$ ti$.$ a$.$ Determine whether the line and the plane intersect. If they do$,$ then find their point of intersection b$.$ Determine whether the point $(0,1,3)$ belongs to the plane or not. c$.$ Determine whether the point $(5,2,3)$ belongs to the line or not. d$.$ Determine whether the given line intersects with the line with equation l$($t$)=$ h$3$t $+3,2$t$,$ t $+1$i$.$