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Unformatted text preview: Section 13.2 Vectors “Direction and Magnitude” 1. Basic Definitions Vectors are one of the main ideas used in multivariable calculus. A vector is a quantity which consists of a direction and a magnitude . The following are all examples: Velocity : direction is which way you are going and magnitude is speed. Force : direction is which was the force is being directed, magnitude is the amount of force Displacement : direction and distance of something moved from one point to another We shall initially deal with displacement vectors because they are easy to understand  however, all the results we shall consider are true of general vectors. There are a number of important definitions and some new terminology we need. ( i ) The displacement vector from point A to point B is an arrow with its tail at A and its tip at B . ( ii ) We call A the initial point and point B the terminal point and denote the vector by vector AB . ( iii ) The magnitude of the vector vector AB is defined to be the length and the direction is the direction in which it points. We denote its magnitude by  vector AB  . ( iv ) Two vectors are considered equivalent or equal if they have the same magnitude and direction (even if they have different initial and end positions). ( v ) The zero vector denotes vector 0 is defined to be the vector of mag nitude 0. We define it to have no direction. For example, in the picture below, vector AB = vector EF but neither are equal to vector CD . A B C D E F We note that when representing a vector by a letter, we shall always include a bar or arrow over it to avoid confusion with scalars (numbers) 1 2 which are just magnitudes  the book does not do this!!! (So u is a number, but vectoru or ¯ u is a vector). 2. Operations on Vectors Just like with numbers, we can define basic arithmetic operations on vectors. There are three basic operations: ( i ) Addition If ¯ u and ¯ v are vectors so the initial point of ¯ v is the end point of ¯ u , we define the sum u + v to be the vector with the initial point the same as ¯ u and the end point the same as ¯...
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This note was uploaded on 10/28/2010 for the course MA 261 taught by Professor Stefanov during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 Stefanov
 Calculus, Multivariable Calculus, Vectors

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