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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). Two vectors sharing the same direction are said to be * codirectional* or

A direction is often represented as a unit vector, the result of dividing a vector by its length. A given direction unit vector can be evaluated at different positions; doing so defines a unit directed line segment (i.e., a bound vector instead of a free vector). 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 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, 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 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 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

Two directions are * obtuse* or

**^**Sometimes,*parallel*and*antiparallel*are used as synonyms of codirectional and opposite, respectively.