Question 3 Let F (x, y, z) = zi + yj+ xk Calculate the flux of F across S, where the normal to S points in the positive x', Y, z directions.

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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ANSWER 3, S is equal to the S in question 1!

Question 1
Let S be the surface that is the part of the plane x + y + z
the first octant. Find a parametrization for S of the form r (x, y), where
(x, y) E R andR is a suitable triangle in the xy-plane.
3 lying in
Question 2
Hence evaluate the scalar surface integral.
x do.
Question 3
Let
F (x, y, z) = zi+ yj+ xk
Calculate the flux of F across S, where the normal to S points in the positive
x, y, z directions.
Transcribed Image Text:Question 1 Let S be the surface that is the part of the plane x + y + z the first octant. Find a parametrization for S of the form r (x, y), where (x, y) E R andR is a suitable triangle in the xy-plane. 3 lying in Question 2 Hence evaluate the scalar surface integral. x do. Question 3 Let F (x, y, z) = zi+ yj+ xk Calculate the flux of F across S, where the normal to S points in the positive x, y, z directions.
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