a$)$ Determine the angle between the vectors vec$(u)=(1,2,3,4)$ and vec$(v)=(0,-1,4,-2)$

b$)$ Given vec$(u)=7$vec$(i)-$vec$(j)$ vec$(k)$ and vec$(v)=-2$vec$(i)5$vec$(j)-6$vec$(k)$ compute $Pro{j}_{\text{v}\text{e}\text{c}(v)}$vec$(u).$

c$)$ Find a vector that is orthogonal to the plane containing the points $P=(3,0,1),Q=(4,-2,1),$ and $R=(5,3,1).$