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lctr05_s12 - 2. F y Important Usea right handed coordinate...

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x y z i j k x y z F F x F y F z 2 2 2 z y x z y x z y x F F F F F F F + + = = + + = + + = F k j i F F F F    § 2.3  Cartesian Vectors in 3-D Important: Use a  right- handed   coordinate  system
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x y z F α β γ α ( θ )    =   angle between  x -axis and  F β    ( θ )    =   angle between  y -axis and  F γ     ( θ z  )    =   angle between z-axis and  F α β  and  γ   are called the  “coordinate direction  angles” more ... Direction angles &  direction cosines
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Direction cosines provide unit vector components 1 cos cos cos | | ) ˆ cos ˆ cos ˆ (cos ˆ 2 2 2 = + + = + + = = z y x v z y x v u k j i v u v v θ θ θ θ θ θ
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x y z F α β γ F x F y F z Example 1 : A pole is  subjected to a force  F  which  has components Fx =1.5 kN  and   Fz =1.25 kN .   If  β  = 75 ° ,   determine the  magnitudes of  F  and  F y. A: F  = 2.02 kN F y = 0.523 kN
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Example 2 :   Determine the  magnitude and  direction angles 
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  • Spring '08
  • Witt
  • position vector, Infiniti FX, cartesian vector representation, unit vector components, Position vector components

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