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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
The directions perpendicular to the galactic plane point to the galactic poles. In actual usage, the terms galactic plane and galactic poles usually refer specifically to the plane and poles of the Milky Way, in which Planet Earth is located. Some galaxies are irregular and do not have any well-defined disk.
The inclination of exoplanets or members of multi-star star systems is the angle of the plane of the orbit relative to the plane perpendicular to the line of sight from Earth to the object. [5] An inclination of 0° is a face-on orbit, meaning the plane of the exoplanet's orbit is perpendicular to the line of sight with Earth.
For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order. A great example of perpendicularity can be seen in any compass, note the cardinal points; North, East, South, West (NESW) The line N-S is perpendicular to the line W-E and the angles N-E, E-S, S-W and W-N are all 90° to one another.
For a spiral galaxy, this can be obtained from the inclination of the galactic plane to the plane of the sky, and the position angle of the major axis as viewed from Earth. The result yields a direction perpendicular to the galactic plane. [1] In the case of the Milky Way, this is given by the coordinates of the galactic pole.
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m, a common perpendicular would have slope −1/m and we can take the line with equation y = −x/m as a common perpendicular ...
Lines perpendicular to line l are modeled by chords whose extension passes through the pole of l. Hence we draw the unique line between the poles of the two given lines, and intersect it with the boundary circle; the chord of intersection will be the desired common perpendicular of the ultraparallel lines.
In a 1981 paper, N. G. de Bruijn investigated special cases of this construction in which the line arrangement consists of sets of equally spaced parallel lines. For two perpendicular families of parallel lines this construction gives the square tiling of the plane, and for three families of lines at 120-degree angles from each other ...