ho we can proof that two lines are coplanar?

let the equation of the lines be 
$$\begin{gathered} \frac{x-x_1}{l_1}=\frac{y-y_1}{m_1}=\frac{z-z_1}{n_1}............\left(1\right) \\ \frac{x-x_2}{l_2}=\frac{y-y_2}{m_2}=\frac{z-z_2}{n_2}............\left(2\right) \end{gathered}$$
therefore the condition that the lines are coplanar is:
$\left|\begin{array}{c}{x}_2-x_1\\ l_1\\ l_2\end{array}\begin{array}{c}{y}_2-y_1\\ m_1\\ m_2\end{array}\begin{array}{c}{z}_2-z_1\\ n_1\\ n_2\end{array}\right|=0$

hope this helps you