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