(c) Let S be a surface described by x² + y² + 3z² = 1, z ≤ 0, and let F(x, y, z)= yi-xj+zx³y²k. Prove that [₁0x) (V x F).dS = 2π

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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(c) Let S be a surface described by x² + y² + 3z² = 1, z ≤ 0, and let
F(x, y, z)=
yirxj+zx³y²k.
Prove that
[(x
(V x F).dS = 2π
Transcribed Image Text:(c) Let S be a surface described by x² + y² + 3z² = 1, z ≤ 0, and let F(x, y, z)= yirxj+zx³y²k. Prove that [(x (V x F).dS = 2π
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