Coordinates of a point, vector or line in space

### 26.10.4 Coordinates of a point, vector or line in space

See Section 25.12.4 for coordinates in two-dimensional geometry.

The coordinates command takes finds the coordinates of a point.

- coordinates takes P, which can be a point (or a sequence or list of points), a vector, or a line.
- If P is a point, then coordinates(P) returns a list consisting of the abscissa, ordinate and cote. If P is a list or sequence of points, then the command returns a list or sequence of such lists.
- If P is a vector, for example from A to B, then coordinates(P) returns a list of the coordinates of B−A.
- If P is a line, then coordinates(P) returns a list of two points on the line, in the order determined by the direction of the line.

#### Examples

coordinates(point(1,2,3))

| ⎡ ⎣ | 1,2,3 | ⎤ ⎦

coordinates(point(0,1,2),point(1,2,4))

| ⎡ ⎣ | 0,1,2 | ⎤ ⎦ | , | ⎡ ⎣ | 1,2,4 | ⎤ ⎦

Note that if the argument is a list of real numbers, it is interpreted as a list of points on the real axis of the plane.

coordinates([1,2,4])

⎡ ⎢ ⎢ ⎣ |
1 | 0
2 | 0
4 | 0
| ⎤ ⎥ ⎥ ⎦

coordinates(vector(point(1,2,3),point(2,4,7)))

| ⎡ ⎣ | 1,2,4 | ⎤ ⎦

coordinates(line(point(-1,1,0),point(1,2,3)))

| ⎡ ⎣ | ⎡ ⎣ | −1,1,0 | ⎤ ⎦ | , | ⎡ ⎣ | 1,2,3 | ⎤ ⎦ | ⎤ ⎦

coordinates(line(x-2*y+3=0, 6*x+3*y-5*z+3=0))

| ⎡ ⎣ | ⎡ ⎣ | −1,1,0 | ⎤ ⎦ | , | ⎡ ⎣ | 9,6,15 | ⎤ ⎦ | ⎤ ⎦