# Vector

From AMS Glossary

## vector

Any quantity, such as force, velocity, or acceleration, that has both magnitude and direction at each point in space, as opposed to a scalar that has magnitude only.

Such a quantity may be represented geometrically by an arrow of length proportional to its magnitude, pointing in the assigned direction. A unit vector is a vector of unit length; in particular, the three unit vectors along the positive Equations written in vector form are valid in any coordinate system. Mathematically, a vector is a single-row or single-column array of functions obeying certain laws of transformation.

*x*,*y*, and*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*a*_{1},*a*_{2}, and*a*_{3}along the coordinate axes*x*,*y*, and*z*, respectively; for example,**A**=*a*_{1}**i**+*a*_{2}**j**+*a*_{3}**k**. 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,*See*scalar product, vector product, Helmholtz's theorem.