A generic displacement vector.Vectors are a useful tool in physics. We use vectors to describe displacements, velocities, accelerations, forces, fields, and many other physical quantities.  These quantities have both a magnitude (size) and a direction.  They are usually depicted as arrows in diagrams.  When we write one, we give it a variable letter, like for displacement.  We put a small arrow over the letter to show that it is a vector.

Why learn about vectors?

In order to do most of the physics in Physics I and Physics II, you need to have a good grasp of the basics of vectors.  Combining them isn’t terribly difficult, but takes a bit more than just adding them algebraically.  As a result of working through this course, you will learn how and when to use vectors. In order to study motion in more than one dimension, we generally break the position, velocity, and acceleration into pieces called components.  These components point along our coordinate system.   If you can find the sides of a triangle, you know how to find components. While finding components initially seems like a chore, it actually helps simplify the situation.  The horizontal pieces and the vertical pieces can be treated separately, and then combined together at the end of the problem.   This is a big help in problems involving two dimensional motion.  You can treat a projectile problem relatively easily by first finding the components of the launch velocity. Let’s learn how to describe these things, break them into pieces, and put them back together again.

Course Objectives

After completing this course, you will be able…
  1.  To describe what a vector is.
  2.  To define the terms vector, magnitude, component.
  3.  To add two vectors using the head-to-tail method.
  4.  To add two vectors using the parallelogram method.
  5.  To multiply a vector by a scalar.
  6.  To break a vector into components.
  7.  To find the magnitude and direction of a vector when given its components.
  8.  To add two or more vectors using components.