Consider the vectors vec$(v)=($:$2,0,-1$:$),$vec$(w)=($:$-1,1,1$:$)$ and vec$(u)=($:$0,3,2$:$).$

a$.$ Find a unit length vector in the direction of vec$(w).$

b$.$ Compute the value vec$(v)*vec(u)-2||vec(w)||.$

c$.$ Find the projection of vec$(u)$ onto vec$(w).$

d$.$ Find the volume of the parallelepiped spanned by vec$(v),$vec$(w)$ and vec$(u).(5$ point per part$)$