$(1)$ Given the points $P(8,2,-1)$ and $Q(1,4,7)$

$(5$ points$)$

a$).$ Find the distance between $P$ and $Q.$

b$)$ Find the vector vec$(PQ)$

c$)$ Find a unit vector in the direction of $,$vec$(PQ)$

d$)$ Find a vector of length $4$ in the direction of vec$(PQ)$

e$).$ Find the value of vec$(PQ)*vec(v)$ where vec$(v)=($:$4,-1,2$:$)$

$(2)$ Sketch a graph of the following surface in R$3.$ Name the surface. Show scale and label axes.

$(5$ points$)$

$z=cosy$

Name of surface: