Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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![Determine if the statements below are True or False. If it's True, explain why. If it's False explain why not, or simply
give an example demonstrating why it's false.
(a) For any vector field F, the gradient of the divergence of F is always zero.
(b) The volume of a solid E is equal to the flux of the vector field (0, 0, z) through the boundary surface.
(c) There exists a vector field F such that ||curl(F)|| = 1 = div(F).
%3|
(d) Let F be a vector field and let G = curl(F). If S is a surface and the flux of G through S is negative, then S
has a non-empty boundary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd921f42-9d02-4a4d-aac8-1dab558085a6%2Fbf118a32-a480-4262-ba78-3a4dabcfe398%2Fp36hup_processed.png&w=3840&q=75)
Transcribed Image Text:Determine if the statements below are True or False. If it's True, explain why. If it's False explain why not, or simply
give an example demonstrating why it's false.
(a) For any vector field F, the gradient of the divergence of F is always zero.
(b) The volume of a solid E is equal to the flux of the vector field (0, 0, z) through the boundary surface.
(c) There exists a vector field F such that ||curl(F)|| = 1 = div(F).
%3|
(d) Let F be a vector field and let G = curl(F). If S is a surface and the flux of G through S is negative, then S
has a non-empty boundary.
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