Chapter 2 - Summary

Chapter 2 - Summary - Addition of Vectors in 2D Represent...

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Addition of Vectors in 2D Addition of Vectors in 3D Represent each vector in Cartesian vector notation: ˆˆ xy FF iF j =+ G Add like components: Rx x Ry y Magnitude of resultant: 22 RR x R y F Direction angle 1 tan Ry Rx F F θ = Represent each vector in Cartesian vector notation: ˆˆˆ xy z jF k =++ G Add like components: Rx x Ry y Rz z = Σ = Σ = Σ Magnitude of resultant: 222 x R y R z F F + Direction cosines cos cos cos y xz F FFF αβγ === G GG Relationship between Direction Cosines and Unit Vector cos cos cos 1 y A A AA A ui j k a n d A A == + + + + = G G G G cos cos cos A u iA jA k k α βγ = G G G G G G
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Position Vector – fixed vector that locates a point in space relative to another point. For example, the position vector between A and B is: ( ) ( ) ( ) ˆˆˆ BA B A B A B A rr r x x i y yj z z k =−= + + GG G Force Directed Along a Line – Often times, forces are directed along lines (i.e. along a rope, chain, or cord). The direction of the force is the same as the unit vector directed in the same sense as the force, as shown below.
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This note was uploaded on 04/17/2008 for the course EGN 3311 taught by Professor Hudyma during the Spring '08 term at UNF.

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Chapter 2 - Summary - Addition of Vectors in 2D Represent...

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