A vector is a quantity that has both magnitude and direction, unlike a scalar, which has only magnitude. Examples of vectors include velocity, acceleration, and force. The velocity of an object is specified by its speed and its direction in which it is moving at any instant. Similarly, a force has both magnitude and direction, hence weight (the force of gravity on a body) is a vector. In contrast, mass and temperature are scalara quantities.


A vector ata point in three-dimensional space is represented by a list of three numbers which give the direction and magnitude (the value of which depends also on the position of the point in question). Geometrically, te three values specify an arrow with direction and magnitude.


Vectors are added when, for instance, movement takes place in a frame of reference that is itself moving (for example, as when a swimmer tries to cross a flowing river). Vectors are added like arrows, end to end, so that in the case of two vectors, the sum is the vector from the tail of the first to the tip of the second. Vectors are a specific type of tensor.


Terms related to vectors


position vector

A vector whose point of origin is the origin of a coordinate system, and whose end-point is some other point. Position vectors cannot, like other vectors, be freely moved parallel to themselves; they are bound to the origin of the coordinate system.


vector field

A set of vectors such that every point in a particular region of space R is associated with a single vector. A familiar example of a vector field in nature is a magnetic field.