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Unformatted text preview: ALL YOU NEED TO KNOW ABOUT VECTORS AND FORCES A vector is a mathematical entity used to describe a physical quantity having both magnitude and direction. You have probably already taken courses involving vector addition and multiplication etc. Here we summarize the important features of vectors that you will need for this course and also try to organize them so that you don’t have so many things to remember. Elementary treatments of vectors are often based on trigonometric meth ods, such as triangles and polygons of forces. These can be useful for visual ization in two dimensions, but threedimensional trigonometry is conceptu ally difficult and almost impossible to represent on the page with intelligable figures. Also trigonometric methods require you to be familiar with the var ious trigonometric identities, such as formulae for compound angles, the sine and cosine rules, etc. We can avoid all this by performing all the necessary operations using algebraic operations rather than trigonometry. Cartesian vectors For this purpose, the first step in almost any vector problem will be to write the vector in terms of its Cartesian components. For example, the vector F in Cartesian coordinates x, y, z can be written F = { F x , F y , F z } . (1) This notation is easy to write and has the added advantage that it is similar to the notation used for vectors in linear algebra classes. The sum of two vectors is obtained by summing the respective Cartesian components. For example F + G = { F x , F y , F z } + { G x , G y , G z } = { ( F x + G x ) , ( F y + G y ) , ( F z + G z...
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This note was uploaded on 10/05/2011 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.
 Fall '07
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