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I’d argue that going 4 m in one direction would be equivalent to going -4 m in the opposite direction. That would eliminate any dependence on interpretation.kuruman said:Suppose one has ##\vec A = 3 \,\hat i - 4 \,\hat j##. I am using specific numbers instead of ##A_x## and ##A_y## to remove the sign ambiguity that is inherent in algebraic symbols.

I see two interpretations for the term ##- 4 \,\hat j## representing the vector component of ##\vec A## in the y-direction.

We teach students to say that vector ##\vec A = 3 \,\hat i - 4 \,\hat j## has a negative y-component, which conforms with interpretation 1, yet in everyday life we conform with interpretation 2. When someone asks us, "which way did he go?", we extend our arm to form a unit vector with its tail at our shoulder and its tip at the end of our index finger and say, "he went that-a-way" whichever way that is. If he went South, we say and point "South" (interpretation 1), we don't say "North moving backwards" (interpretation 2.) Small wonder there is confusion.

- A vector of negative y-component pointing in +y-direction, i.e. ##- 4 \,\hat j=(-4)(+\hat y).##
- A vector of positive magnitude 4 pointing in the negative y direction, i.e. ##- 4 \,\hat j=(+4)(-\hat y).##

Just a few thoughts ##\dots##