Right-handed coordinate system

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SUMMARY

A right-handed coordinate system is defined rigorously by the condition that the cross product of the unit vectors x-hat and y-hat equals the unit vector z-hat, expressed mathematically as x-hat × y-hat = z-hat. This definition is contrasted with a left-handed coordinate system, where the relationship is x-hat × y-hat = -z-hat. Understanding these definitions is crucial for applications in physics and engineering, where the orientation of coordinate systems affects calculations and interpretations.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with cross product operations
  • Basic knowledge of coordinate systems
  • Concept of unit vectors
NEXT STEPS
  • Study vector cross product properties in depth
  • Explore applications of right-handed and left-handed coordinate systems in physics
  • Learn about transformations between different coordinate systems
  • Investigate the implications of coordinate system orientation in 3D modeling software
USEFUL FOR

Students in physics or engineering, mathematicians, and anyone involved in 3D modeling or computer graphics who needs a clear understanding of coordinate system orientations.

ehrenfest
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Homework Statement


Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet.

Is this true:

A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat

?

Homework Equations





The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
ehrenfest said:
A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat

Yes.
In a left-handed system, \hat{x} \times \hat{y}= - \hat{z}
 

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