parallelism of line and plane
Parallelity of a line and a plane means that the angle between line and plane is 0, i.e. the line and the plane have either no or infinitely many common points.
So, . If , we can set a set along the parallel lines and another plane . The common points of and are on the intersection line of the planes. If would intersect the plane , then it would intersect also the line , contrary to the assumption. Thus .
Theorem 2. If a plane is set along a line () which is parallel to another plane (), then the intersection line () of the planes is parallel to the first-mentioned line.
Proof. The lines and are in a same plane, and they cannot intersect each other since otherwise would intersect the plane which would contradict the assumption. Accordingly, .
|Title||parallelism of line and plane|
|Date of creation||2013-03-22 18:47:58|
|Last modified on||2013-03-22 18:47:58|
|Last modified by||pahio (2872)|