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What is the meaning of path independence of a vector field F? O The vector field assumes the same values on any two paths between two fixed points. - ○ F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. O None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.

What is the meaning of path independence of a vector field F? O The vector field assumes the same values on any two paths between two fixed points. - ○ F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. O None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.

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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What is the meaning of path independence of a vector field F? The vector field assumes the same values on any two paths between two fixed points. ○ F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.
Transcribed Image Text:What is the meaning of path independence of a vector field F? The vector field assumes the same values on any two paths between two fixed points. ○ F(Q) – F(P) has the same value for all points P and Q in the domain of the vector field. None of the given choices All line integrals of F (over any path) have the same value. O All line integrals of F between two fixed points have the same value.
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