# Vector fields and integral curves

by meteorologist1
Tags: curves, fields, integral, vector
 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 $$\alpha$$ a positive function on R^n. Express the integral curves of the vector field $$\alpha K$$ in terms of those of K. And why did we require that $$\alpha$$ be positive? Thanks in advance.

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