Vector algebra I Scaling and adding vectors
This chapter explains what a displacement vector is and utilizes vector notation and the arrow representation of a vector. It describes geometrical figures and spatial relationships in terms of linear combinations of vectors. The chapter examines a vector equation is equivalent to three scalar equations for the components. Many of the quantities of interest in physics and engineering can be classified as scalars or vectors. A scalar is a quantity that is specified completely by a single number and a physical unit of measure. The chapter is concerned with vector algebra, and discusses the study of how vectors mathematically and how vectors can be added, subtracted and multiplied. The magnitude and direction of the resultant of two or more vectors can often be found by using Pythagoras’s theorem and elementary trigonometry. The chapter reviews the three-dimensional Cartesian coordinate systems and the Cartesian coordinates of a point. It shows how the Cartesian components of a vector are defined.