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

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In a right-handed system where vectors A, B, and C are orthogonal and of unit length, the relationship A x B = C holds true, along with B x C = A and C x A = B. For a general case, A, B, and C maintain a right-handed orientation if the triple scalar product (A x B) . C is positive. This means that if A x B equals C, then the scalar product (A x B) . C results in a positive value, confirming the right-handed nature of the system. The discussion clarifies the conditions under which these vector relationships apply. Understanding these principles is essential for vector analysis in physics and mathematics.
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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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