* + iy (excluding the stagnation3. Let F(r, y, 2) = (0,0, z) and let S be the portion of the paraboloid s=1-above and including the r-y plane with normal n pointing upwardsnegative z-coordinate).(a) Find a parametrisation of the surface S with normal n pointing upwardh(b) Use the parametrisation from part (3a) to calculate(F n) dS.(c) Find a parametrisation of the boundary of S.Hint: show that the boundary of S is the circle z + y = 1, z = 0.(d) Use Stokes' theorem and the parametrisation for part (3c) to calculaten) dS.cos 0 de = 0.Given: curl(0, , 0) = (0,0, 2) and

Using parametrization and Stoke's theorem

*+iy (excluding the stagnation 3. Let F(x, y, z) = (0, 0, a) and let S be the portion of the paraboloid :=1-2²-²2² negative 2-coordinate). (.e. non- (a) Find a parametrisation of the surface 5 with normal n pointing upwards. (b) Use the parametrisation from part (3a) to calculate (F-n) ds. (c) Find a parametrisation of the boundary of S. Hint: show that the boundary of S is the circle x² + y² = 1, z = 0. (d) Use Stokes' theorem and the parametrisation for part (3c) to calculate n) ds. 2m cos³0 de = 0. Given: curl(0,²,0) = (0,0,r) and JL.F.

*+iy (excluding the stagnation 3. Let F(x, y, z) = (0, 0, a) and let S be the portion of the paraboloid :=1-2²-²2² negative 2-coordinate). (.e. non- (a) Find a parametrisation of the surface 5 with normal n pointing upwards. (b) Use the parametrisation from part (3a) to calculate (F-n) ds. (c) Find a parametrisation of the boundary of S. Hint: show that the boundary of S is the circle x² + y² = 1, z = 0. (d) Use Stokes' theorem and the parametrisation for part (3c) to calculate n) ds. 2m cos³0 de = 0. Given: curl(0,²,0) = (0,0,r) and JL.F.

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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