ABSTRACT
A vector can be assigned to the tangent space defined at a point. Similarly, another vector may be assigned to the tangent space of a neighboring point. In this way, we can assign vectors to all point of the manifold. In mathematics, a vector field is a mapping rule which assigns a vector to each point in a subspace. Using a local coordinate system of a manifold, continuity and differentiability of vector fields are defined. Vector fields are often used to model the speed and direction of a moving fluid or the magnitude and direction of force, such as magnetic or gravitational force.
