question_answer

The length of the perpendicular from the origin to the plane passing through the point a and containing the line\[\vec{r}=\vec{b}+\lambda \,\vec{c}\], is __.

A)  \[\frac{[\vec{a}\vec{b}\vec{c}]}{|\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}|}\]

B)  \[\frac{[\vec{a}\vec{b}\vec{c}]}{|\vec{a}\times \vec{b}+\vec{b}\times \vec{c}|}\]

C)  \[\frac{[\vec{a}\,\vec{b}\,\vec{c}]}{|\vec{b}\times \vec{c}+\vec{c}\times \vec{a}|}\]

D)  \[\frac{[\vec{a}\,\vec{b}\,\vec{c}]}{|\vec{c}\times \vec{a}+\vec{a}\times \vec{b}|}\]