In a two-dimensional vector field, each point (x, y) in the plane is associated with a vector  V(x, y) = P(x, y)i + Q(x, y)j, where P and Q are scalar functions of x and y, and i and j are the unit vectors in the x and y directions, respectively. In a three-dimensional vector field, each point (x, y, z) in space is associated with a vector  V(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k, where P, Q, and R are scalar functions of x, y, and z, and i, j, and k are the unit vectors in the x, y, and z directions, respectively.