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Statics For Dummies by James H. Allen, III, PE, PhD

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Chapter 5. Using Vectors to Better Define Direction

After you have a handle on how to graphically represent all the information required to accurately depict a vector, you're ready to begin tackling different methods for putting vectors to work. The first step is representing the vector in mathematical terms. In this chapter, I describe the notation required to do just that and then show some of the basic calculations that are essential in the vector creation process.

I also show you how to create several basic vectors and even how to use vectors to create additional vectors. All these techniques add more ammunition to your proverbial vector toolbox and are especially essential for simplifying three-dimensional statics problems down the road.

Taking Direction from the Cartesian Coordinate System

The majority of the basic problems that you solve involve the Cartesian coordinate system, so the following list introduces you to several important terms related to that system. You can also check out Figure 5-1 for a look at how they work together.

  • Axis: The axes are the reference lines that act as a simple ruler for measuring distances of points or objects from a user-defined reference point, known as the origin, which I discuss later in this section. In two dimensions, you use two axes: an x-axis and a y-axis. ...

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