ch11 - Math 241 Chapter 11 Dr. Justin O. Wyss-Gallifent §...

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Unformatted text preview: Math 241 Chapter 11 Dr. Justin O. Wyss-Gallifent § 11.1 Cartesian Coordinates in Space 1. Preliminaries: How to plot points in 3-space, the coordinate planes, the first octant. Emphasize how perspective can be confusing at first. 2. Distance between points: | PQ | = radicalbig ( x 1 − x ) 2 + ( y 1 − y ) 2 + ( z 1 − z ) 2 3. Equation of a circle, a closed disk, a sphere and a closed ball. Pictures of all. § 11.2 Vectors in Space 1. Definition of a vector as a triple of numbers. The notation ¯ a or → a . We can add and subtract vectors by adding and subtracting components and we can multiply a scalar by a vector by multiplying by all the components. Three special vectors are ˆ ı = (1 , , 0), ˆ = (0 , 1 , 0) and ˆ k = (0 , , 1). Then every vector can be written as ¯ a = a 1 ˆ ı + a 2 ˆ + a 3 ˆ k . Vectors are not necessarily anchored anywhere though often we anchor them somewhere (the origin, for example) for some reason. 2. Basic properties and associated definitions: (a) The zero vector is ¯ 0 = 0ˆ ı + 0 ˆ + 0 ˆ k ....
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.

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ch11 - Math 241 Chapter 11 Dr. Justin O. Wyss-Gallifent §...

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