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Unformatted text preview: Chapter 3: Euclidean Vector Spaces Section 3.1: Vectors in 2-Space, 3-Space, and n-Space A vector is described by a numerical value with a direction. Representation of vectors: 1. Geometrically: described by initial and terminal points 2. Algebraically: described by coordinates (usefull for calculations) Example: Displacement vector: Edmonton- 2712 km Toronto Vectors with the same length and same direction are called equivalent. Addition and Substraction: We have a triangle rule: Given vectors % v and w to find v + w position the vector w so that its initial point coincides with the terminal point of v. The vector v + w is represented by the arrow from the initial point of v to the terminal point of w. We have the zero vector = vector of length 0 and denoted by 0 (0= (initial point=terminal point)). We have 0 + v = v + 0 for every vector v. Substraction: For vector- v consider -- v then w- v = w + (- v ) Hence v + (- v ) = 0 ....
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This note was uploaded on 04/27/2011 for the course ENGR 130 taught by Professor Zhang during the Spring '11 term at University of Alberta.
- Spring '11