vector quantity

Any physical quantity that has both magnitude (size) and direction, such as velocity, acceleration, or force, as distinct from a scalar quantity such as speed, density, or mass, which has magnitude but no direction. A vector is represented either geometrically by an arrow whose length corresponds to its magnitude and points in an appropriate direction, or by two or three numbers representing the magnitude of its components. Vectors can be added graphically by constructing a parallelogram of vectors (such as the parallelogram of forces commonly employed in physics and engineering). This will give a resultant vector.

The position vector of a point A(x,y) represents the move from the origin to A, that is a translation. A free vector has magnitude and direction but no fixed position in space.

If two forces p and q are acting on a body at A, then the parallelogram of forces is drawn to determine the resultant force and direction r. p, q, and r are vectors. In technical writing, a vector is denoted by bold type, underlined, or overlined.