What is a Vector?

What is a vector? Mathematically, it is an abstract representation of a quantity with multiple dimensions. To represent this quantity, we may use an arrow (graphically), or an ordered set of values (numerically). Unlike scalar quantities such as temperature, vector quantities—things like displacement or force—must be represented in two or three (or possibly even more) dimensions. An important question, then, is to consider what makes a “vector” representation of a quantity so useful to us? One advantage is that we can break down these vectors into their components—their basic dimensional elements. By doing this, we can take two seemingly unrelated vectors (such as two forces pulling the same object in two unrelated directions), and combine them. We accomplish this by breaking each vector down into its set of components; effectively, we re-create the two different vectors as sums of differently scaled versions of the same standard set of vectors. Then, with the two vectors expressed in terms of the same kinds of components, we add up these separate parts of each vector that are related. If you have ever added two vectors in a physics class, then you have had experience with this operation before.

Return to the vector – signal analogy table.

Discovery Project II. Vaz, Richard F. 2001. WPI. 14 June 2002

<http://www.ece.wpi.edu/courses/ee2311/temp/dp2.htm>