Use Stokes' to calculate surface integral $$ \iint_{S}\operatorname{curl}\mathbf{F} \cdot d\mathbf{S} \,,$$ where $ \mathbf{F} = \langle z,x,y\rangle $ and $\mathbf{S}$ is the surface pictured below. The boundary curve C, is oriented clockwise.
That's what the problem calls for. My questions are: 1) How do I parameterize the surface so as to know what numbers to take. 2) Why do we care about the orientation?