2. True/False: If F, G are vector fields and V × F = V × G, then F = G. (Justify your answer by using the properties of curl.) 3. True/False: If F is conservative then V · F = 0. (Justify your answer.)

2. True/False: If F, G are vector fields and V × F = V × G, then F = G. (Justify your answer by using the properties of curl.) 3. True/False: If F is conservative then V · F = 0. (Justify your answer.)

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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Question

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Please answer question 2 and 3 for this homework. Thanks

1. True/False: V (V × F) = 0. (Justify your answer by showing it is true or false
for vector fields of the form F Fi+ Gj.)
2. True/False: If F, G are vector fields and V × F = V x G, then F = G. (Justify
your answer by using the properties of curl.)
3. True/False: If F is conservative then V F 0. (Justify your answer.)
4. True/False: curl(divF)) is not a meaningful expression. (Justify your answer.)
5. Using Stokes' theorem, find I = | [,(V × F)-ndo , where F
and S is the portion of the surface 2.x -+ y + z = 2 above the first octant and n is
the unitary normal vector to the surface, with non-negative z component.
yi + rj+(y+ z) k

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