Parallel lines and planes in space: parallel

### 14.5.5 Parallel lines and planes in space: parallel

See Section 13.7.5 for parallel lines in the plane.

The parallel command can take its arguments in different ways. It returns and draws a line or plane depending on the arguments.

A point and a line.

- parallel takes two arguments:
  - P, a point.
  - L, a line.
- parallel(P,L)returns and draws the line through P parallel to L.

Example.
Input:

parallel(point(1,1,1),line(point(0,0,0),point(0,0,1)))

Output:

Two non-parallel lines.

- parallel takes two arguments:
  L,M, two lines which aren’t parallel.
- parallel(L,M)returns and draws the plane containing L which is parallel to M.

Example.
Input:

parallel(line(point(1,0,0),point(0,1,0)),line(point(0,0,0),point(0,0,1)))

Output:

A point and a plane.

- parallel takes two arguments:
  - P, a point.
  - PL, a plane.
- parallel(P,PL) returns and draws the plane through P that is parallel to PL.

Example.
Input:

parallel(point(0,0,0),plane(point(1,0,0),point(0,1,0),point(0,0,1)))

Output:

A point and two non-parallel lines.

- parallel takes three arguments:
  - P, a point.
  - L,M, two non-parallel lines.
- parallel(P,L,M) returns and draws the plane through P that is parallel to L and M.

Example.
Input:

parallel(point(1,1,1),line(point(0,0,0),point(0,0,1)),line(point(1,0,0),point(0,1,0)))

Output: