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I have always handled the plus or minus sign problem in one dimensional
situations as follows.
1) Begin with an introductory (just addition and subtraction) exposition of
3 dimensional (Cartesian) vectors. Introduce and freely use the unit vectors
I, j and k.
2) Impart some facility by working examples in two dimensions,
geometrically and algebraically. Explicitly use unit vectors.
3) Go to one dimension, working examples always using the unit vector i.
Use vector addition and subtraction, geometrically and algebraically.
4) Carefully notice that in one dimensional algebraic expressions the unit
vector is superfluous (it can be cancelled out of any equation, or taken out
of any expression as a common factor). The only directionality to be
specified is forward or backward, and that is just as unambiguously handled
by signed numbers ( + vs - ) as by signed unit vectors( +I vs -i). So in
the interest of conservation of ink/chalk, we can drop the unit vectors from
one dimensional vector situations and simply use the convenient notation of
signed numbers. Emphasize that the unit vector (i) is still implicit (as an
overall common factor) in these one dimensional expressions. Beginners
might be encouraged to still explicitly write each one dimensional vector as
a magnitude with a signed unit vector - until it becomes "natural" to infer
the absent unit vector.
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
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