# Checking if lines and/or planes in space are perpendicular: is_perpendicular

### 14.13.4 Checking if lines and/or planes in space are perpendicular: is_perpendicular

See Section 13.16.12 for checking for perpendicularity in two-dimensional geometry.

The is_perpendicular command determines if two objects are perpendicular.

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

Note that two lines must be coplanar to be perpendicular.

#### Examples.

- Input:
  is_perpendicular(line([2,3,-2],[-1,-1,-1]),line([1,0,0],[1,2,8]))
  Output:

  0

- Input:

  P1:= plane([0,0,0],[1,2,-3],[1,1,-2])
  P2:= plane([-1,-1,-1],1,2,-3],[0,0,0])
  is_perpendicular(P1,P2)

  Output:

  1

- Input:

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

  Output:

  0