In geometry , direction , also known as spatial direction or vector direction , is the common characteristic of all rays which coincide when translated to share a common endpoint; equivalently, it is the common characteristic of vectors (such as the relative position between a pair of points) which can be made equal by scaling (by some positive scalar multiplier ).
6-508: Forward is a relative direction , the opposite of backward. Forward may also refer to: Relative direction Two vectors sharing the same direction are said to be codirectional or equidirectional . All co directional line segments sharing the same size (length) are said to be equipollent . Two equipollent segments are not necessarily coincident; for example, a given direction can be evaluated at different starting positions , defining different unit directed line segments (as
12-404: A bound vector instead of a free vector ). A direction is often represented as a unit vector , the result of dividing a vector by its length. A direction can alternately be represented by a point on a circle or sphere , the intersection between the sphere and a ray in that direction emanating from the sphere's center; the tips of unit vectors emanating from a common origin point lie on
18-469: A common point. The direction of a non-oriented line in a two-dimensional plane, given a Cartesian coordinate system, can be represented numerically by its slope . A direction is used to represent linear objects such as axes of rotation and normal vectors . A direction may be used as part of the representation of a more complicated object 's orientation in physical space (e.g., axis–angle representation ). Two directions are said to be opposite if
24-504: The unit sphere . A Cartesian coordinate system is defined in terms of several oriented reference lines, called coordinate axes ; any arbitrary direction can be represented numerically by finding the direction cosines (a list of cosines of the angles) between the given direction and the directions of the axes; the direction cosines are the coordinates of the associated unit vector. A two-dimensional direction can also be represented by its angle , measured from some reference direction,
30-474: The angular component of polar coordinates (ignoring or normalizing the radial component). A three-dimensional direction can be represented using a polar angle relative to a fixed polar axis and an azimuthal angle about the polar axis: the angular components of spherical coordinates . Non-oriented straight lines can also be considered to have a direction, the common characteristic of all parallel lines , which can be made to coincide by translation to pass through
36-467: The unit vectors representing them are additive inverses , or if the points on a sphere representing them are antipodal , at the two opposite ends of a common diameter. Two directions are parallel (as in parallel lines ) if they can be brought to lie on the same straight line without rotations; parallel directions are either codirectional or opposite. Two directions are obtuse or acute if they form, respectively, an obtuse angle (greater than
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