Vector algebra II Scalar and vector products
This chapter explains the geometric definition of the scalar product to calculate the scalar product of two given vectors. It examines algebraic expressions involving the scalar product and utilizes the scalar product to determine the magnitude of a given vector and the angle between two given vectors. The chapter is concerned with products of vectors. There are two useful ways in which a product can be formed from two vectors. One is called the scalar product because the product so formed is a scalar quantity; the other is called a vector product because the product is itself another vector. Vector products can be manipulated algebraically according to rules that are similar to those of ordinary number algebra except that the vector product is non-commutative and there is no division by a vector. The chapter illustrates scalar products and vector products in a scientific context by worked examples and problems.