27.4.1  Lines and directed lines in space

See Section 26.6.1 for lines in the plane.

The line command returns and draws a directed line. It can take its arguments in three different ways.

1. Two points.
   • line takes two arguments: P,Q, two points (which can also be given as a list).
   • line(P,Q) returns and draws the line whose direction is from the P to Q.
2. A point and a direction vector.
   • line takes two arguments:
     • P, a point.
     • [u₁,u₂,u₃], a direction vector.
   • line(P,[u₁,u₂,u₃]) returns and draws the line through the given point with the direction given by the direction vector.
3. Two planes.
   • line takes two arguments: eqn₁,eqn₂, the equations of two planes.
   • line(eqn₁,eqn₂) returns and draws the line which is the intersection of the planes.
   • The direction of this line is given by the cross-product of the normals for the planes. For example, the intersection of the planes x=y (normal (1,−1,0)) and y=z (normal (0,1,−1)) will be (1,−1,0)× (0,1,−1)=(1,1,1).

Examples