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Unformatted text preview: ALL YOU NEED TO KNOW ABOUT VECTORS AND FORCES Cartesian vectors We define vectors in terms of their Cartesian components F = { F x , F y , F z } . (1) The sum of two vectors is obtained by summing the respective Cartesian components. For example F + G = { ( F x + G x ) , ( F y + G y ) , ( F z + G z ) } . (2) The magnitude of a vector  F  is defined by  F  = q F 2 x + F 2 y + F 2 z . (3) Unit vectors A unit vector is a vector with unit magnitude. It will generally be denoted by the symbol e = { e x , e y , e z } . (4) It follows from the definition that  e  = e 2 x + e 2 y + e 2 z = 1 . (5) However, we use the special notation i , j , k for unit vectors aligned with the x , y , or z coordinate axes respectively. Notice that with this notation i = { 1 , , } ; j = { , 1 , } ; k = { , , 1 } . (6) A general vector can be defined in terms of magnitude and direction by the product F = e  F  , (7) where e is a unit vector in the same direction as F . From this equation, we see that e =...
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This note was uploaded on 08/30/2008 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.
 Fall '07
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