I don't really disagree with what Joel Rauber has said. However, the
original questioner was asking if there are techniques to help students
"get the right direction" for vectors.
In my experience, following the conventions I outlined in my first
response is the technique I have found useful. Bright students can
solve problems lots of ways and avoid common mistakes. Average
students, and especially below-average students need to see problems
solved systematically and then practice solving problems systematically
themselves. Deciding which triangle to draw and which angles to use is
something that can baffle some students for a long time... as in
forever. Yes, I wish they could get to the point that they can see the
problem from many viewpoints and realize there are multiple ways to do
the trig. But, as the original questioner stated... that just isn't
happening. Therefore, if I can adopt a standard way of doing things
that can be taught and understood by average students who are willing to
try it, then you bet I am going to use and advocate that method.
Therefore, it is not so much that I have some "standard conventions"
ingrained in my mind that we have to follow, as it is that I am trying
to get the bulk of my class to have success.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu