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Three line segments with the same direction. 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 ...
When only the magnitude and direction of the vector matter, and the particular initial or terminal points are of no importance, the vector is called a free vector. The distinction between bound and free vectors is especially relevant in mechanics, where a force applied to a body has a point of contact (see resultant force and couple ).
The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...
Given a subset S of R n, a vector field is represented by a vector-valued function V: S → R n in standard Cartesian coordinates (x 1, …, x n).If each component of V is continuous, then V is a continuous vector field.
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
The use of motion lines in art is similar to the lines showing mathematical vectors, which are used to indicate direction and force. A similar effect is found in long-exposure photography, where a camera can capture lights as they move through time and space, blurred along the direction of motion.
Vector images resulted from mathematical geometry . In mathematical terms, a vector consists of both a magnitude, or length, and a direction. Often, both raster and vector elements will be combined in one image; for example, in the case of a billboard with text (vector) and photographs (raster). Example of vector file types are EPS, PDF, and AI.
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .