Direction and signs of unit vectors

AI Thread Summary
Negative quantities in vector notation can be interpreted as direction changes rather than negative magnitudes. Specifically, a negative quantity pointing in the positive z direction is equivalent to a positive quantity pointing in the negative z direction, represented mathematically as -A\hat{z} = A\hat{-z}. This equivalence highlights that vectors have directionality and magnitude, but do not possess negative magnitudes. Understanding this concept is crucial for correctly interpreting vector operations and their representations. Thus, the direction of a vector is essential in determining its equivalence to another vector with a different sign.
warfreak131
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If I have a negative quantity pointing in the positive z direction, is that the same as a positive quantity pointing in the negative z direction?

e.g.

does -A\hat{z}=A\hat{-z}?
 
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yes they are the same
 
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