Graphing a vector with component angles?

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SUMMARY

The discussion focuses on graphing a resultant vector R with component angles θx, θy, and θz. The user seeks clarification on how to visualize this vector given its components . The method involves using the dot product of the vector R with unit vectors along the x, y, and z axes to derive the angles. Specifically, the equations Rx = |R|cosθx, Ry = |R|cosθy, and Rz = |R|cosθz are established as the basis for graphing the vector accurately.

PREREQUISITES
  • Understanding of vector notation and components
  • Familiarity with the dot product in vector mathematics
  • Knowledge of unit vectors in three-dimensional space
  • Basic trigonometry, specifically cosine functions
NEXT STEPS
  • Study vector visualization techniques in 3D space
  • Learn about the dot product and its applications in physics
  • Explore graphical software tools for vector representation, such as GeoGebra
  • Investigate the relationship between vector components and angles in more complex scenarios
USEFUL FOR

Students in physics or mathematics, educators teaching vector analysis, and anyone interested in mastering vector graphing techniques.

Psych Berry
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At the end of a problem (I'm sure I did all the math correctly, that's not an issue) I'm supposed to graph the corresponding resultant vector. However, along with the magnitude of the vector, the angles given are in component form: θx, θy, θz. I've never encountered this before, and although it seems like it's probably easy, I have no idea how to graph such a vector. Can anyone explain how, or is there anything anyone knows of that I can use a reference?
 
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Say your vector is R, with components as such <Rx,Ry,Rz>. To get the angle R makes with the x-axis, you'd dot product R with <1,0,0> (unit vector in direction of the x-axis).

This gives
<Rx,Ry,Rz>.<1,0,0>=|R|(1)cosθx

Or simply Rx=|R|cosθx

Do a similar exercise with the unit vectors in the direction of the y and z axes to get the components Ry and Rz
 

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