Engineering Calculus Notes 95

Engineering Calculus Notes 95 - A B C , with vertices A =...

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1.6. CROSS PRODUCTS 83 The (orthogonal) projection of points in R 3 to a plane P takes a point P R 3 to the intersection with P of the line through P perpendicular to P (Figure 1.43 ). We denote this by b P b proj P P P Figure 1.43: Projection of a Point P on the Plane P P = proj P P. Similarly, a vector −→ v is projected onto the direction of the line where the plane containing −→ v and the normal to P meets P (Figure 1.44 ). −→ v proj P −→ v P Figure 1.44: Projection of a Vector −→ v on the Plane P Suppose ABC is an oriented triangle in R 3 ; its projection to P is the oriented triangle
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Unformatted text preview: A B C , with vertices A = proj P A , B = proj P B , and C = proj P C . What is the relation between the oriented areas of these two triangles? Let P be the plane containing ABC and let n be the unit vector (normal to P ) such that V A ( ABC ) = A n where A is the area of ABC . If the two planes P and P are parallel, then A B C is a parallel translate of ABC , and the two oriented areas...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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