# Lines and directed lines in space: line

### 14.5.1 Lines and directed lines in space: line

See Section 13.7.1 for lines in the plane.

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

Two points:

- line can take 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.

#### Example.

Input:

line([0,3,0],point(3,0,3))

Output:

A point and a direction vector.

- line can take 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.

#### Example.

Input:

line([0,3,0],[3,0,3])

Output:

Two planes.

- line can take 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).

#### Example.

Input:

line(x=y, y=z)

Output: