Relative direction (geometry) in the context of "Radial velocity"

In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies.More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement, in which case it may be necessary to add an imaginary translation to change the object's position (or linear position). The position and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its position does not change when it rotates.

Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representing the orientation using an axis–angle representation. Other widely used methods include rotation quaternions, rotors, Euler angles, or rotation matrices. More specialist uses include Miller indices in crystallography, strike and dip in geology and grade on maps and signs.A unit vector may also be used to represent an object's normal vector direction or the relative direction between two points.

The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observer/spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken note of or to be taken note of by the observer, at any distance more than least distance of distinct vision. In optics, refraction of a ray due to use of lenses can cause distortion. Shadows, patterns and movement can also influence line of sight interpretation (as in optical illusions).

The term "line" typically presumes that the light by which the observed object is seen travels as a straight ray, which is sometimes not the case as light can take a curved/angulated path when reflected from a mirror, refracted by a lens or density changes in the traversed media, or deflected by a gravitational field. Fields of study feature specific targets, such as vessels in navigation, marker flags or natural features in surveying, celestial objects in astronomy, and so on. To have optimal observational outcome, it is preferable to have a completely unobstructed sightline.

In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction between two points. If the two points are at the same level (relative to a specific datum), the slant distance equals the horizontal distance.

An example of slant range is the distance to an aircraft flying at high altitude with respect to that of the radar antenna. The slant range (1) is the hypotenuse of the triangle represented by the altitude of the aircraft and the distance between the radar antenna and the aircraft's ground track (point (3) on the earth directly below the aircraft). In the absence of altitude information, for example from a height finder, the aircraft location would be plotted further (2) from the antenna than its actual ground track.