Vectors

This chapter focuses on vectors, or physical quantities that require both magnitude and direction for their specification, such as velocity, force, electric field, magnetic field, and displacement. It underscores that vector notation and vector algebra are important for the formulation and solution of physical problems in three dimensions, specifically in mechanics, fluid dynamics, electromagnetic theory, and engineering design. The chapter discusses in examples some of the uses of vectors that are important in molecular dynamics, spectroscopy, and theoretical chemistry. It shows how a vector is graphically represented by a directed line segment. It also gives an overview of vector algebra. Furthermore, it discusses the components of vectors. The chapter progresses to explain the scalar differentiation of a vector, scalar product, and vector product. It also tackles the scalar and vector fields, the gradient of a scalar field, divergence and curl of a vector field, and vector spaces.