We have already seen the difference between scalar and vector quantities. We know that a scalar is just a number, while a vector is a number (the magnitude of the vector) and a direction.  We have also seen that important quantities such as displacement, velocity, and acceleration are all vector quantities, while your height, your age, and your mass are all scalar quantities.  Until now, we have really dealt with only one-dimensional vectors — that is, vectors lying along a straight line (which we called the x-axis or the y-axis).

In this lecture we will take a more careful and complete look at vectors and the arithmetic of vectors. This will involve being introduced to some basic definitions and ideas in trigonometry.  We will then use these basic definitions to help us find the components of vectors, and to perform vector arithmetic.  The next lecture will then apply these topics to the study of 2-D motion.