Calculating with Vectors

Vectors are denoted by bold-faced letters (upper case, lower case, or Greek) in most books,

But it is hard to draw bold faced letters in chalk on the blackboard. So most people use arrows to indicate vectors. In this class we also follow this convention, because it is then visually very easy to identify vector quantities:

, , , ..., , , , ..., , , , ...

The length of a vector will be designated by the absolute value symbol:

|| means the length of the vector . This is often just called A.

There are two methods for adding and subtracting vectors, the graphical and the analytic (or component).

1. Graphical method ("tail to head" method).
   When adding for example, + = , we put the tail of on the head of . is then the vector from the tail of to the head of .

    

2. Component method. Here we find the Cartesian components of each vector and add them independently.

We will use the first method (the graphical) to illustrate problems, but the second method is the only way to obtain numerical answers except for a few special cases.

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