# Current Affairs JEE Main & Advanced

## Coplanar Lines

Category : JEE Main & Advanced

Lines are said to be coplanar if they lie in the same plane or a plane can be made to pass through them.

Condition for the lines to be coplanar:

If the lines $\frac{x-{{x}_{1}}}{{{l}_{1}}}=\frac{y-{{y}_{1}}}{{{m}_{1}}}=\frac{z-{{z}_{1}}}{{{n}_{1}}}$ and $\frac{x-{{x}_{2}}}{{{l}_{2}}}=$ $\frac{y-{{y}_{2}}}{{{m}_{2}}}=$ $\frac{z-{{z}_{2}}}{{{n}_{2}}}$ are coplanar, then $\left| \,\begin{matrix} {{x}_{2}}-{{x}_{1}} & {{y}_{2}}-{{y}_{1}} & {{z}_{2}}-{{z}_{1}} \\ {{l}_{1}} & {{m}_{1}} & {{n}_{1}} \\ {{l}_{2}} & {{m}_{2}} & {{n}_{2}} \\ \end{matrix}\, \right|=0$.

The equation of the plane containing them is  $\left| \,\begin{matrix} x-{{x}_{1}} & y-{{y}_{1}} & z-{{z}_{1}} \\ {{l}_{1}} & {{m}_{1}} & {{n}_{1}} \\ {{l}_{2}} & {{m}_{2}} & {{n}_{2}} \\ \end{matrix}\, \right|=0$ or $\left| \,\begin{matrix} x-{{x}_{2}} & y-{{y}_{2}} & z- {{z}_{2}} \\ {{l}_{1}} & {{m}_{1}} & {{n}_{1}} \\ {{l}_{2}} & {{m}_{2}} & {{n}_{2}} \\ \end{matrix}\, \right|=0$.

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