Condition for Coplanarity of Two Lines in Vector Form
If the lines $\overrightarrow{\mathit{r}}=\overrightarrow{{\mathit{a}}_1}+\mathit{\lambda }\overrightarrow{{\mathit{b}}_1}$ and $\overrightarrow{\mathit{r}}=\overrightarrow{{\mathit{a}}_2}+\mathit{\mu }\overrightarrow{{\mathit{b}}_2}$ are coplanar,
then $\overrightarrow{\mathit{r}}\bullet \left(\overrightarrow{{\mathit{b}}_1}\times \overrightarrow{{\mathit{b}}_2}\right)=\overrightarrow{{\mathit{a}}_2}\bullet \left(\overrightarrow{{\mathit{b}}_1}\times \overrightarrow{{\mathit{b}}_2}\right)$
Substituting above values in this equations