# Planes orthogonal to lines and lines orthogonal to planes in space: orthogonal

### 14.5.7 Planes orthogonal to lines and lines orthogonal to planes in space: orthogonal

The orthogonal command finds orthogonal objects. It takes its arguments in different ways, and returns and draws a line or plane, depending on the arguments.

A point and a line.

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

#### Example.

Input:

orthogonal(point(0,0,0),line(point(1,0,0),point(0,1,0)))

Output:

A line and a plane.

- orthogonal takes two arguments:
  - L, a line.
  - P, a plane.
- orthogonal(L,P) returns and draws the plane containing L that is perpendicular to P.

#### Example.

Input:

perpendicular(line(point(0,0,0),point(1,1,0)),
plane(point(1,0,0),point(0,1,0),point(0,0,1)))

Output: