Right-Handed System: AxB=C or CxA=B?

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SUMMARY

The discussion centers on the properties of vectors A, B, and C in a right-handed system. It establishes that A x B = C, B x C = A, and C x A = B when A, B, and C are orthogonal unit vectors. Furthermore, it clarifies that the right-handedness of A, B, and C can be determined by the positivity of the triple scalar product (A x B) · C, applicable even when the vectors are not orthogonal or of unit length. This definitive relationship is crucial for understanding vector orientation in three-dimensional space.

PREREQUISITES
  • Understanding of vector operations, specifically cross product and dot product.
  • Familiarity with the concept of right-handed systems in vector mathematics.
  • Knowledge of scalar triple products and their geometric interpretations.
  • Basic proficiency in linear algebra and vector spaces.
NEXT STEPS
  • Study the properties of the cross product in three-dimensional vector spaces.
  • Learn about the scalar triple product and its applications in determining vector orientation.
  • Explore the implications of right-handed and left-handed systems in physics and engineering.
  • Investigate the geometric interpretations of vector products in various coordinate systems.
USEFUL FOR

This discussion is beneficial for students and professionals in mathematics, physics, and engineering, particularly those dealing with vector analysis and three-dimensional geometry.

phymatter
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if we say that A , B and C form a right handed system , where all 3 are vectors then does it mean that A X B = C or C X A = B ??
pl. help !
 
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If A, B, and C are at right angles to one another, and have length 1, then that specific order, A, B, C, is a "right hand system" if and only if A x B= C, B x C= A, and C x A= B.
 
thanks HallsofIvy !
 
in general (not orthogonal, not unit length) you might say that A,B,C in that order is right-handed iff the triple scalar product (A x B) . C is positive.
 
g_edgar said:
in general (not orthogonal, not unit length) you might say that A,B,C in that order is right-handed iff the triple scalar product (A x B) . C is positive.

hi g_edgar!

how does this relate to the previous rule :"If A, B, and C are at right angles to one another, and have length 1, then that specific order, A, B, C, is a "right hand system" if and only if A x B= C, B x C= A, and C x A= B. "
 
If A x B= C then (A x B) . C= C . C which is positive.
 

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