Understanding Right and Left Handed Systems in Vector Calculus

[laminatedevildoll]

If a, b, c are right handed system, then so are b, c, a, and c, a, b. In this case, the vectors a, c, b and c, b, a and b, a, c are a left handed system.

In order to prove the above statement, I know that the right handed system is positive and the left handed system is negative. So for the second part, b,c,a and c, a, b are right handed because the positions were switched two times, so that makes a right handed system. But, a, c, b and c, b, a and b, a, c are only switched once, so that makes a left handed system. Is this how I prove this statement?

 

[mathwonk]

first you need a definition of right handed and left handed. what is it? or of orientation - preserving. then just check that these cases obey the definition.

 

[laminatedevildoll]

This is not a formal definition but, when the determinant is negative, it's left handed and if it's positive, it's right handed.