In its simplest form, a vector is a directed line segment. Physical quantities, such as velocity, acceleration, force, and displacement, are vector quantities, or simply vectors, because they can be represented by directed line segments. The algebra of vectors was initiated principally through the works of W. R. Hamilton and H. G. Grassmann in the middle of the nineteenth century, and brought to the form presented here by the efforts of O. Heaviside and J. W. Gibbs in the late nineteenth century. Vector analysis is a tool of the mathematical physicist, because many physical laws can be expressed in vector form.