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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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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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