If curl f everywhere perpendicular to the z-axis and if c

Question

Question: 1. If curl F^→ everywhere perpendicular to the z-axis, and if C is a circle in the xy-plane, then the circulation of F^→ around C is zero.

2. If S is the upper unit hemisphere x² + y² + z² = 1, z ≥ 0, oriented upward, then the boundary of S used in Stokes' Theorem is the circle x² + y² = 1, z = 0, with orientation counterclockwise when viewed from the positive z-axis.