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Unformatted text preview: a l c u l a ti n g a n y th i n g ? Can you predict the magnitude of the cross product without calculating a n y th i n g ? I did it Example: find the area of the parallelogram spanned by and Compute the cross product! Phew! Hmmm.... Maybe drawing a picture of this (the parallelogram and the cross product) would help you cement this in your mind. Exploratory probe Suppose you model a surface with a computer: you can't do continuous or smooth things, so the surface is modeled as having a ton of faces (like the facets of a demonic gem). These faces might be described with coordinates in . How can you find the normal vector to one of the faces? How many ways are there to make a normal vector? Is it unique? Can you use them to distinguish "inside" from "outside"? Use the internet to find out if these things come up outside of math class! Next: lines and planes!...
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