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9.1 - Visualizing the xyz coordinate system 
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<h2>9.1 - Visualizing the xyz coordinate system</h2>
<p class="noprint">Pick up 3 pipe cleaners of different colors. <img src="0g/9.2.pipecleaners.jpg" class="rightalign"> 
<ul class="noprint"><li>Twist one end of each together, with the 3 sticking out at 90 degrees from each other. 
<li>Kink an "arrow" onto the end of the one you're calling $\uv z$.
<li>Kink a ball onto the end of the one you're calling $\uv x$.
<li>Write down your color key indicating $\hat x, \hat y, \hat z$ in order for these to form a <i>right-handed coordinated system</i>, that is, $\hat x \times \hat y = \hat z$. <b>Confirm your key with your instructor before going on</b>.
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<p><img src="0g/9.1.visualize1.gif" alt="" width="935" height="619"><br>
<img src="0g/9.1.visualize2.gif" alt="" width="935" height="469">
<h4>Use GeoGebra to confirm your *point of view*</h4>
<p class="show incremental"><b>Try this</b> in GeoGebra: Create a point called "PNP" (get it??)<br>
<img src="0g/PNP.png"><br>
Now, rotate the coordinate system around with your mouse until the point PNP appears to be directly <i>on top</i> of the origin.  Now you are looking at the origin from a point which has a coordinate like $(+k,-k,+k)$ (where $k$ is some positive constant).
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