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

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Discussion Overview

The discussion revolves around the properties of vectors A, B, and C in the context of right-handed systems. Participants explore the relationships between these vectors, particularly focusing on the cross product and the conditions under which the vectors form a right-handed system. The scope includes theoretical considerations and mathematical reasoning regarding vector orientation and scalar products.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether A x B = C or C x A = B when A, B, and C form a right-handed system.
  • Another participant states that if A, B, and C are orthogonal and of unit length, the order A, B, C is a right-handed system if and only if A x B = C, B x C = A, and C x A = B.
  • A participant suggests that in a general case (not necessarily orthogonal or unit length), A, B, C is right-handed if the triple scalar product (A x B) . C is positive.
  • Another participant reiterates the condition regarding the triple scalar product and seeks clarification on its relation to the earlier rule about orthogonal vectors.
  • A participant notes that if A x B = C, then (A x B) . C = C . C, which is positive.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the definitions and conditions for a right-handed system, particularly in relation to orthogonality and the scalar product. The discussion remains unresolved as no consensus is reached on the implications of the different conditions presented.

Contextual Notes

Participants highlight limitations in their discussions, such as the dependence on specific conditions (orthogonality, unit length) and the need for clarity regarding the implications of the scalar product in different contexts.

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 !
 
Mathematics news on Phys.org
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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