# Show a flowline of a vector field?

1. Mar 7, 2012

### Suy

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)=(e8t+e−8t, e8t−e−8t, e2t) is a flowline for the vector field F.

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

Now consider the curve r(t)=(cos(8t), sin(8t), e2t) . 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)) = (8e8t-8e-8t,8e8t-8e-8t,2e2t)

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

2. Mar 7, 2012

### HallsofIvy

Staff Emeritus
Re: Show a flowline of a vector field??

Okay, and do you understand why that is "(8y, 8x, 2z)"?

Do the same thing. If $r(t)= (x, y, z)= (cos(8t), sin(8t), e^{2t})$ what is $r'(t)$? What is that in terms of x, y, and z?

3. Mar 7, 2012

### Suy

Re: Show a flowline of a vector field??

Thanks for the reply!! It definitely helped me understanding the question!!! And I know how to do it now!