Vector Operations and Matlab
The following is a supplementary source for reviewing and understanding the basic
concepts of vector manipulation as it relates to Statics. This review is engineering in
nature but will be presented in a more casual manner in hopes of clarifying and
simplifying the subject matter. For a more in-depth review, consult a Statics book.
What is a vector?
In the simplest terms, a vector is nothing more than a line with a specified direction and
magnitude. The direction can be described either through coordinates or angles. An
easy example of a vector quantity is velocity of a car. If you are driving 75 mph due
West then you just described a vector. If you are driving 75 mph on I-80 then you have
described a scalar because only magnitude is known, direction is not specified. A vector
can be written in many different ways. Depending on how you were taught, a vector may
be identified by either an arrow over the top of a character or a line below a character as
shown below:
Aor A
Figure 1. Vector Symbols
In this tutorial, vectors will be denoted by a line below their character.
The direction of a vector can be described in two main ways: a vector can be described
by an associated angle or through x-y-z components. The two systems for describing the
direction of a vector are compatible. If the x-y-z components are known then the angle
can be calculated and visa versa.
An often confusing concept for people new to working with vectors is the notation. In
introductory engineering classes, the axis are labeled x, y, and z. The vector directions
associated with the x, y, and z directions are i, j, and k. Why are the directions not x, y,
and z? Who knows?!?! The longer you are in engineering the more notation systems you
will learn. Each notation system has its place and will prove to be useful but will often
seem irrelevant and confusing until you reach more advanced engineering classes.
How to deal with vectors?
Working with vectors is not complicated. There are only a couple of tricks to remember.
1.) Vector addition and subtraction always occurs tip to tail. This means that when
adding vectors you align the vectors of interest so that the tail of one vector
touches the tip of the previous. The resultant vector is drawn from the tail of the
first vector to the tip of the last. Several examples are shown below.
