What is a vector ?

One of the most important and fundamental concepts in linear algebra is the vector. Luckily, vectors are all around us, but they are, in general, not visible. The common ways to introduce a vector is either to begin with the strict mathematical definition, or to discuss examples of vectors, such as velocities, forces, acceleration, etc. A vector is a mathematical quantity with both magnitude and direction. The magnitude of vector u, denoted |u|, is it's length. One way to express its direction is to give the angle it makes with a horizontal ray (that points to the right) that is parallel to the positive x-axis. This is called the vector's direction angle.