This chapter considers both finite- and infinite-dimensional vectors. Using the Dirac notation and shows that some cases can be conceptually treated in similar fashions. Very basic results from vector calculus in two-dimensional (2-D) are used to solve the problem of planetary motion. A vector in 2-D is defined by its length and the angle it makes with a reference axis. This vector is represented graphically by an arrow. The tail of the arrow is called the initial point of the vector and the tip of the arrow is the terminal point. The negative of a vector is that vector whose tip and tail have been exchanged from those of the vector. MATLAB distinguishes between two kinds of vectors: the column vector and the row vector. As long as the components of the vectors are all real, the difference between the two is in the structure of the array.