Unformatted text preview: x y z b b b A B C igure 1.41: Oriented Triangle in R 3 A (2 , 3 , 4), B (4 , 2 , 5), and C (3 , 1 , 3); from our point of view (we are looking from moderately high in the Frst octant), the orientation appears counterclockwise. By interpreting ( A,B,C ) as a unit normal vector, we associate to an oriented triangle ABC R 3 an oriented area v A ( ABC ) = ( A,B,C ) A ( ABC ) represented by a vector normal to the triangle whose length is the ordinary area of ABC . Note that for a triangle in the xyplane, this means...
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 Fall '08
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 Calculus, Dot Product, Standard basis, Unit Normal Vector

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