The 3 - The 3-D Coordinate System Well start the chapter...

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The 3-D Coordinate System We’ll start the chapter off with a fairly short discussion introducing the 3-D coordinate system and the conventions that we’ll be using. We will also take a brief look at how the different coordinate systems can change the graph of an equation. Let’s first get some basic notation out of the way. The 3-D coordinate system is often denoted by . Likewise the 2-D coordinate system is often denoted by and the 1-D coordinate system is denoted by . Also, as you might have guessed then a general n dimensional coordinate system is often denoted by . Next, let’s take a quick look at the basic coordinate system. This is the standard placement of the axes in this class. It is assumed that only the positive directions are shown by the axes. If we need the negative axis for any reason we will put them in as needed. Also note the various points on this sketch. The point P is the general point sitting out in 3-D space. If we start at P and drop straight down until we reach a z -coordinate of zero we arrive at the point Q . We say that Q sits in the xy -plane. The xy -plane corresponds to all the points which have a zero z -coordinate. We can also start at P and move in the other two directions as shown to get points in the xz -plane (this is S with a y -coordinate of zero) and the yz -plane (this is R with an x -coordinate of zero). Collectively, the xy , xz , and yz -planes are sometimes called the coordinate planes. In the remainder of this class you will need to be able to deal with the various coordinate planes so make sure that you can.
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The 3 - The 3-D Coordinate System Well start the chapter...

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