Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z).c(t) = (sin(t), cos(t), 3e¹); F(x, y, z) = (y, −x, z)(cos(t), – sin(t), 3e¹)c'(t)F(c(t))==Since c'(t) = vF(c(t)), we have shown that c'(t) is a flow line of F.

We have to show the following conditions according to the given information

Answered: Show that the given curve c(t) is a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 25E

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Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z). c(t) = (sin(t), cos(t), 3e¹); F(x, y, z) = (y, -x, z) (cos(t), - sin(t), 3e¹) c'(t) = F(c(t)) = Since c'(t) X F(c(t)), we have shown that c'(t) is a flow line of F.