Let S Be the Parametric Surface $\vec { r } ( s , t ) = s \cos t \vec { i } + s \sin t \vec { j } + \left( s ^ { 2 } - s \sin t \right) \vec { k }$

Essay

Let S be the parametric surface $\vec { r } ( s , t ) = s \cos t \vec { i } + s \sin t \vec { j } + \left( s ^ { 2 } - s \sin t \right) \vec { k }$ for $0 \leq s \leq 2$ , $0 \leq t \leq 2 n$ .
(a)What does the projection of S onto the xy-plane look like?
(b)Show that S is part of the surface $z = x ^ { 2 } + y ^ { 2 } - y$ .
(c)Find a unit vector that is normal to the surface at the point (1,2,3).