Let F= (y-r, z²+y) and C be the closed, piece-wise smooth curve in the zy-plane consisting of: C: the directed line segment from (a,0) → (a, a), followed by C: the directed line segment from (a, a) → (0, a), followed by; C3: the path along the quarter circle + y² = a? from (0, a) -→ (a,0). a) For what values of a >0 is fF. dr = 0? b) Is the line integral f.F- dr path-independent on R?? Explain.

Let F= (y-r, z²+y) and C be the closed, piece-wise smooth curve in the zy-plane consisting of: C: the directed line segment from (a,0) → (a, a), followed by C: the directed line segment from (a, a) → (0, a), followed by; C3: the path along the quarter circle + y² = a? from (0, a) -→ (a,0). a) For what values of a >0 is fF. dr = 0? b) Is the line integral f.F- dr path-independent on R?? Explain.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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