# The length of $\perp$ from origin to the plane passing through the point $\overrightarrow a$ and containing the line $\overrightarrow r=\overrightarrow b+\lambda \overrightarrow c$ is ?

$\begin{array}{1 1} (a)\:\large\frac{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]}{|\overrightarrow a\times \overrightarrow b+\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a|}\: & \:(b)\:\large\frac{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]}{|\overrightarrow a\times \overrightarrow b+\overrightarrow b\times\overrightarrow c||} \\ (c)\:\large\frac{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]}{|\overrightarrow b\times\overrightarrow c+\overrightarrow c\times\overrightarrow a|}\: & \:(d)\:\large\frac{[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]}{|\overrightarrow a\times \overrightarrow b+\overrightarrow c\times\overrightarrow a|} \end{array}$

• Vector equation of a plane through the point $\overrightarrow a$ and with normal $\overrightarrow n$ is $(\overrightarrow r-\overrightarrow a).\overrightarrow n=0$