(adsbygoogle = window.adsbygoogle || []).push({}); Show a flowline of a vector field??

1. The problem statement, all variables and given/known data

Consider the vector field F(x,y,z)=(8y,8x,2z).

Show that r(t)=(e^{8t}+e^{−8t}, e^{8t}−e^{−8t}, e^{2t}) is a flowline for the vector field F.

r'(t)=F(r(t)) = (_,_,_)

Now consider the curve r(t)=(cos(8t), sin(8t), e^{2t}) . It is not a flowline of the vector field F, but of a vector field G which differs in definition from F only slightly.

G(x,y,z)=(_,_,_)

2. Relevant equations

3. The attempt at a solution

I guess the first part of the question r'(t)=F(r(t)) = (8e^{8t}-8e^{-8t},8e^{8t}-8e^{-8t},2e^{2t})

For the second part, I don't understand the question... hope someone can explain to me?

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# Show a flowline of a vector field?

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