Using the general formula for the vector surface element, \begin{equation} d\SS = d\rr_1 \times d\rr_2 \label{dr1dr2} \end{equation} find explicit formulas for the vector surface element in each of the following cases:

• a plane in both rectangular and polar coordinates;
• the three surfaces (top, bottom, and curved side) of a cylinder with finite length;
• the surface of a sphere.