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Vector fields and integral curves

by meteorologist1
Tags: curves, fields, integral, vector
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Jan10-05, 07:06 PM
P: 101
I'm studying about vector fields and integral curves in the space R^n.

I need some help in proving or getting some comments/feedback on the following propositions:

1) Find a proof or counterexample: Let K and K' be two vector fields on R^n such that every integral curve of K is also an integral curve of K'. Then K = K'.

2) State and prove a theorem to the effect that integral curves of a vector field can never cross.

3) Let K be a vector field, and [tex] \alpha [/tex] a positive function on R^n. Express the integral curves of the vector field [tex] \alpha K [/tex] in terms of those of K. And why did we require that [tex] \alpha [/tex] be positive?

Thanks in advance.
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