Given velocity vector {\vec {u}}=(u_x,u_y,u_z) the streamlines is a bunch of curves {\vec {r}}_s = \big( \, x_s, \, y_s, \, z_s \, \big) \in \mathbb{R}^3, parametrized by real number s, and solving the following equation:
| \frac{ d {\vec r}_s}{dt} \times {\vec r}_s(t) = 0 |
or equivalently
| {dx_s \over u_x} ={dy_s \over u_y}={dz_s \over u_z} |