CHAPTER 1 Mathematics

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We've found a method for adding collinear vectors and another one for adding perpendicular vectors. Most situations lie somewhere in between. For example, a displacement east followed by one north of east could not be solved by either method. Instead we'll use a combination of both. Here's the method in a nutshell.

1. Break each vector apart into its x and y-components.
   Ex. A_x, B_x, A_y, B_y
2. Add the collinear x-components to produce Rx.
   Ex. R_x = A_x + B_x
3. Add the collinear y-components to produce R_y.
   Ex. R_y = A_y + B_y
4. R_x & R_y are two perpendicular components of R. Use trigonometric methods to add them.

Here's an example using this method. Please note that although this is a long process with lots of details, it's nothing more than the set of 4 steps above. If you understand the big picture, (the 4 steps above), the details will more naturally follow.