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Let a vector field given by V=V x W where W is an arbitrary vector field. O is always potential O V is never potential. OV has its divergence always strictly negative. OV has its divergence zero. O V has its divergence always strictly positive.

Let a vector field given by V=V x W where W is an arbitrary vector field. O is always potential O V is never potential. OV has its divergence always strictly negative. OV has its divergence zero. O V has its divergence always strictly positive.

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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**Understanding Vector Fields** Consider a vector field given by \( \vec{V} = \nabla \times \vec{W} \) where \( \vec{W} \) is an arbitrary vector field. Here are some properties to consider for \( \vec{V} \): - \( \vec{V} \) is always potential. - \( \vec{V} \) is never potential. - \( \vec{V} \) has its divergence always strictly negative. - \( \vec{V} \) has its divergence zero. - \( \vec{V} \) has its divergence always strictly positive. The aim is to determine the correct property of the vector field \( \vec{V} \) based on its expression.
Transcribed Image Text:**Understanding Vector Fields** Consider a vector field given by \( \vec{V} = \nabla \times \vec{W} \) where \( \vec{W} \) is an arbitrary vector field. Here are some properties to consider for \( \vec{V} \): - \( \vec{V} \) is always potential. - \( \vec{V} \) is never potential. - \( \vec{V} \) has its divergence always strictly negative. - \( \vec{V} \) has its divergence zero. - \( \vec{V} \) has its divergence always strictly positive. The aim is to determine the correct property of the vector field \( \vec{V} \) based on its expression.
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