What is vector algebra?
As we learned on the previous page, vectors alone have limited use other than providing a simple, yet effective, means of displaying quantities possessing both a magnitude and direction. The real power in vectors resides in the ability to perform mathematical operations on them.
An algebra is a set of mathematical rules. And in order to use vector algebra, you have to know the rules. Fortunately for life science majors, there is only one rule you have to remember -- the rule for adding two vectors together. (We will see that the operation of subtraction is essentially the same as addition. And if you can add two vectors together, then adding three or more vectors is straightforward.)
Those studying a calculus-based physics course also have to consider how to multiply vectors, but we will not concern ourselves with this added burden. So vector algebra is actually simpler than regular algebra because we only have to concern ourselves with one operation -- addition.
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Notation and Definitions
We need notation for labeling vectors: A vector is denoted by a bold-face letter, and its length is denoted by the same letter without the bold face.
We now need to introduce a definition: The sum of two or more vectors is another vector called the resultant vector.
Vector addition for two vectors A and B is simply denoted A + B. Therefore, the equation C = A + B simply means "C is the resultant vector obtained by adding vector A to vector B." Vector subtraction of vector B from vector A is simply denoted A - B.
There are three ways to add vectors. Each method will be illustrated using Java applets in the following pages. Naturally, all three methods must produce the same result.
The head-to-tail and parallelogram methods are actually identical, as a Java applet will later demonstrate. They only provide a rough description of the resultant vector, but they are very easy to apply. The component method is used in those situations where exact, numerical information about the resultant vector is required.