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... Yes, Serway does use the two vectors Ax and Ay - however, he is
careful not to use the word "component" until he actually defines the term
from the scalar lengths of those vectors. Then he drops the vectors Ax and Ay
completely throughout the remainder of the text and only uses scalar
components. I think his presentation could have been even stronger by leaving
out those two vectors entirely - I think that was your objection and I agree
with you. Do you have favorite textbooks that you feel take a clearer
approach? ...