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A line of flux of a vector field F is a vectorial curve r(t) that satisfies equality dr F(r(t)) dt If F represents the velocity field of a particle, then the lines of flux they correspond to the paths made by the particle If r(t) = (e2t, In\t|,-),t > 0 then verify that r (t) is a line of flux of the vector field F (x, y, z) = (2x, z, –z²)

A line of flux of a vector field F is a vectorial curve r(t) that satisfies equality dr F(r(t)) dt If F represents the velocity field of a particle, then the lines of flux they correspond to the paths made by the particle If r(t) = (e2t, In\t|,-),t > 0 then verify that r (t) is a line of flux of the vector field F (x, y, z) = (2x, z, –z²)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 12P
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A line of flux of a vector field F is a vectorial curve r(t) that satisfies equality dr = F(r(t)) dt If F represents the velocity field of a particle, then the lines of flux they correspond to the paths made by the particle If r(t) = (e2", In|t|,:), t >0 then verify that r (t) is a line of flux of the vector field F (x, y, z) = (2x, z, –z?)
Transcribed Image Text:A line of flux of a vector field F is a vectorial curve r(t) that satisfies equality dr = F(r(t)) dt If F represents the velocity field of a particle, then the lines of flux they correspond to the paths made by the particle If r(t) = (e2", In|t|,:), t >0 then verify that r (t) is a line of flux of the vector field F (x, y, z) = (2x, z, –z?)
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