The length of the perpendicular from the origin to the plane passing through the point a→ and containing the line  r→=b→+λc→ is

The given plane passes through  a→ and is parallel to the vectors b→−a→ and c→  So it is normal to (b→−a→)×c→ Hence, its equation is (r→−a→)⋅((b→−a→)×c→)=0or r→⋅(b→×c→+c→×a→)=[a→b→c→]The length of the perpendicular from the origin to this plane is [a→b→c→]|b→×c→+c→×a→|