Review of Vectors

$$\centerline{\epsfbox{mathematics.1.eps}}$$ (5.1)

Most motion is not along a straight line. If fact, almost no motion is along a line. We therefore need to be able to describe motion along multiple dimensions (usually 2 or 3). That is, we need to be able to consider and evaluate vector trajectories, velocities, and accelerations. To do this, we must first learn about what vectors are, how to add, subtract or decompose a given vector in its cartesian coordinates (or equivalently how to convert between the cartesian, polar/cylindrical, and spherical coordinate systems), and what scalars are. We will also learn a couple of products that can be constructed from vectors.

A bf vector in a coordinate system is a directed line between two points. It has magnitude and direction. Once we define a coordinate origin, each particle in a system has a position vector (e.g. - $\vec{A}$) associated with its location in space drawn from the origin to the physical coordinates of the particle (e.g. - ($A_x,A_y,A_z$)):

$$\vec{A} = A_x \hat{x} + A_y \hat{y} + A_z \hat{z}$$ (5.2)