Let vec$(a)=(1,2,-1),$vec$(b)=(-1,-1,4).$

$[10$ marks$]$

a$)$ Find $2$vec$(a)-3$vec$(b)$

b$)$ Find vec$(a)*vec(b)$

c$)$ Let vec$(c)=(3,-1,k).$ Find $k$ given that vector vec$(c)$ is perpendicular to vector vec$(a).$

d$)$ Find $2$ vectors that are collinear to vector vec$(b)$

e$)$ Find the projection vector of vec$(a)$ onto vec$(b)$