Parallel lines and planes in space

### 27.4.5 Parallel lines and planes in space

See Section 26.6.5 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.

1. With 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.
2. With 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.
3. With 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.
4. With 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.

#### Examples

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

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

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

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