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Any quantity, such as force, velocity, or acceleration, which has both magnitude and direction at each point in space, as opposed to a scalar which has magnitude only. Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. </dd>
A unit vector is a vector of unit length; in particular, the three unit vectors along the positive X-, Y-, Z-axes of rectangular Cartesian coordinates are denoted, respectively, by i, j, and k. Any vector A can be represented in terms of its components, a1, a2, and a3 along the coordinate axes X, Y, and Z, respectively; e.g., A = a1 + a2 + a3. A vector drawn from a fixed origin to a given point (X, Y, Z) is called a position vector and is usually symbolized by r; in rectangular Cartesian coordinates,

r = xi + yj + zk

Equations written in vector form are valid in any coordinate system. Mathematically, a vector is a single-row or -column array of functions obeying certain laws of transformation. See scalar product, vector product, tensor, Helmholtz theorem.
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This article is based on NASA's Dictionary of Technical Terms for Aerospace Use