   Intersecting Lines
  Is there an equation that will calculate if 2 lines on the same plane intersect? these lines are in 3d space with length from points p1(x,y,z) to p2(x,y,z) and p3(x,y,z) to p4(,y,z)?if not, then is there an equation or formula which can calculate whether or not a point p1(x,y,z) is inside of triangle p2,p3,p4(x,y,z) on the same plane? 
  Closest distance between 2 lines in 3D:http://astronomy.swin.edu.au/~pbourke/geometry/lineline3d/if they intersect then the distance will be 0 (or more likely, close to 0).Determining if a point lies on the interior of a polygon:http://astronomy.swin.edu.au/~pbourke/geometry/insidepoly/look at Solution 4... thats for 3D;  you can create a plane aligned with one edge (say, [p2, p4], and trhe cross product of the two edges ((p2 - p1) x (p4 - p3)), and do a segment / plane intersection (segment [p1, p2] with plane [p3, ((p2 - p1) x (p4 - p3)) x (p4 - p3)].line / plane intersection is easy. 