\(\dfrac{{x - a}}{{{x_0}}} = \dfrac{{y - b}}{{{y_0}}} = \dfrac{{z - c}}{{{z_0}}}\)

\(\dfrac{{x - {x_0}}}{{{x_0}}} = \dfrac{{y - {y_0}}}{{{y_0}}} = \dfrac{{z - {z_0}}}{{{z_0}}}\)

\(\dfrac{{x - {x_0}}}{a} = \dfrac{{y - {y_0}}}{b} = \dfrac{{z - {z_0}}}{c}\)   

\(\left\{ \begin{array}{l}x = {x_0} + at\\y = {y_0} + bt\\z = {z_0} + ct\end{array} \right.\left( {t \in \mathbb{R}} \right)\)