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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.)

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.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 70EQ
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Please answer question 1 and 5 only for this homework. Thank you
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 = J ], (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 + xj+(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 = J ], (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 + xj+(y+ z)k
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