Vector Operations

A vector u is defined as a quantity possessing both a magnitude and a direction; the said magnitude is regularly denoted by u, while information on the direction is often conveyed graphically —–or else encompasses angles formed with the axes in some reference system. A more convenient way of handling vectors resorts, however, to their decomposition along the three directions of space in a typical Cartesian. This chapter provides information on the addition of vectors, multiplication of scalar by vector, scalar multiplication of vectors, and vector multiplication. It provides the mathematical equation and a detailed explanation for each type. The chapter also presents a graphical analysis that emphasizes that the scalar product of two vectors is equivalent to the area of a rectangle, with one side defined by one such vectors and another side defined by the normal projection of the other vector onto the former.