Two lines r = a₁ + λb₁ and r = a₂ + μb₂ are coplanar if and only if

1. Two lines are coplanar when the vector joining a point on one to a point on the other lies in the plane spanned by their directions. 2. That plane has normal b₁ × b₂. 3. The connecting vector (a₂ - a₁) must be perpendicular to this normal. 4. The condition is (a₂ - a₁) · (b₁ × b₂) = 0. _Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.7_