Question

I'm trying to find the field lines, r=(x(t),y(t),z(t)), of F(x,y,z)=(y-z,-x,x-y). Am I supposed to use the formula:
\[\dot{\underline{r}}(t)=\lambda(\underline{r}(t))\underline{F}(\underline{r}(t))\]
for some scalarfield lambda? How does it work?

Answer 1

F(x,y,z)=(y-z,z-x,x-y)

Answer 2

I don't recognize this formula, is it some kind of graphical way to represent div and curl of a vector field?

Answer 3

\[\dot{\underline{r}}(t)=(\frac{dx(t)}{dt},\frac{dy(t)}{dt},\frac{dz(t)}{dt})\]
So I think you're supposed to get a system of differential equations. The line underneath letters means that they're vectors by the way. If you have a different formula, I'm open to ideas.