Question

multivariable calc:
I have a vector \( \vec{v} \). It looks like you can somehow come up with a parameterized curve \( \vec{p} \) that moves in the direction of \( \vec{v} \).

\[ \vec{v} = \begin{bmatrix} a(x,y) \\b(x,y) \\ f(x,y,u) \end{bmatrix} \]

How do I get the parameterization \(\vec{p}(t) = \begin{bmatrix} x(t) \\y(t) \\ u(t) \end{bmatrix} \)