parametric equation of line from vector and point

Given vector $\vec{u}$ and point $(x_0,y_0,z_0)$, a parametric equation for a line can be found:

$$\begin{array}{rl}x& =x_0+u_x\cdot t\\ y& =y_0+u_y\cdot t\\ z& =z_0+u_z\cdot t\end{array}$$