Coordinates of a point, vector or line in space

See Section 26.12.4 for coordinates in 2D 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.

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])

⎡
⎢
⎢
⎣

⎤
⎥
⎥
⎦

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

⎤
⎦