14.13.3  Checking if lines and/or planes in space are parallel: is_parallel

See Section 13.16.11 for checking for parallels in two-dimensional geometry.

The is_parallel command determines if two objects are parallel.

• is_parallel takes two arguments:
  L,P, each one either a line or a plane.
• is_parallel(L,P) returns 1 if L and P are parallel and returns 0 otherwise.

Examples.

• Input:

  L1:= line([0,0,0],[-1,-1,-1])

  L2:= line([2,3,-2],[-1,-1,-1])

  is_parallel(L1,L2)

  Output:

  0

• Input:

  P:= plane([-1,-1,-1],[1,2,-3],[0,0,0])

  is_parallel(P,L2)

  Output:

  1

• Input:

  P1:= plane([0,0,0],[1,2,-3],[1,1,-2])

  P2:= plane([1,1,0],[2,3,-3],[2,2,-2])

  is_parallel(P1,P2)

  Output:

  1