Attached is a document with two sample vector diagrams. A critique of
certain aspects of the drawing mode is inside of the document. :-)
--
Karl Hegbloom <[EMAIL PROTECTED]>
<TeXmacs|1.0.5.11>
<style|generic>
<\body>
<\hide-preamble>
<assign|vec|<macro|v|<with|mode|math|math-font-family|bf|<arg|v>>>>
</hide-preamble>
<center|<larger|<strong|Sample Vector Diagrams>><\footnote>
Copied from ``<em|Calculus Concepts and Contexts>'', second edition,
2001, by <name|James Stewart>, Brooks/Cole publishing.
</footnote>>
The trouble I had in creating these diagrams was that there is not any way
to construct the vectors at specific angles, with specific lengths, and
drawn with their tail anchored to a specific point. I really like the way I
can construct this kind of diagram using XEucleides or DrGeo.
What I had to do is draw the two arrowed lines in the same direction,
parallel to one another, to get the lengths right. Then, I moved the angled
line over, and used the ``rotate'' mode to turn it to about the right
angle. In the second diagram, the lengths are right, but it's unlikely that
the angle is actually <with|mode|math|150<rsup|\<circ\>>> as it should be.
Ideally, a student should be able to take a protractor, measure the angle,
and get the angle as shown. The other problem was then getting the ends of
the vectors aligned the way they should be.
There was also some trouble with editing the labels. I've created a macro
called ``vec'' that typesets the vector variable in upright bold. When I
type the macro and activate it, I'm inside a light blue box where I type
the variable name. Normally, in running text math mode, I type a C-f or
right-arrow to move out of the blue box and back to the rest of the
expression. In drawing mode, however, when I type one of those keys, the
picture slides over. I'd like for the picture keybindings to be shadowed by
the text and math-mode ones while I'm inside of a text box. Positioning the
diagram with arrow keys is great, though I would like to have finer-grained
movements, perhaps by holding Shift or Ctrl while pushing the arrow key.
<hrule>
<no-indent><strong|2--3:> Find <with|mode|math|\|<vec|u>\<times\><vec|v>\|>
and determine whether <with|mode|math|<vec|u>\<times\><vec|v>> is directed
into the page or out of the page.
<paragraph|�9.4 Ex.
2><with|gr-mode|<tuple|edit|line>|gr-frame|<tuple|scale|1cm|<tuple|0.599998gw|0.499997gh>>|gr-geometry|<tuple|geometry|5.20006cm|2.55004cm|center>|gr-grid|<tuple|empty>|gr-edit-grid-aspect|<tuple|<tuple|axes|none>|<tuple|1|none>|<tuple|10|none>>|gr-edit-grid|<tuple|empty>|gr-line-arrows|<tuple|<with|dash-style|none|<line|<tuple|-10ln|6ln>|<tuple|0ln|0ln>|<tuple|-10ln|-6ln>>>>|gr-color|blue|gr-line-width|2ln|gr-as-visual-grid|off|gr-grid-aspect-props|<tuple|<tuple|axes|#808080>|<tuple|1|#c0c0c0>|<tuple|10|#e0e0ff>>|gr-grid-aspect|<tuple|<tuple|axes|#808080>|<tuple|1|#c0c0c0>|<tuple|10|#e0e0ff>>|<graphics|<with|color|blue|line-width|2ln|line-arrows|<tuple|<with|dash-style|none|<line|<tuple|-10ln|6ln>|<tuple|0ln|0ln>|<tuple|-10ln|-6ln>>>>|<line|<point|-1.9|-1.3>|<point|-1.9|1.2>>>|<text-at|<with|mode|math|60<rsup|\<circ\>>>|<point|-1.78467|-0.842334>|left|bottom>|<text-at|<with|mode|math|\|<vec|u>\|=5<vec|
>>|<point|-2.98106|0.0580939999999999>|left|bottom>|<text-at|<with|mode|math|\|<vec|v>\|=10>|<point|-0.398713|-0.682746>|left|bottom>|<with|color|blue|line-width|2ln|line-arrows|<tuple|<with|dash-style|none|<line|<tuple|-10ln|6ln>|<tuple|0ln|0ln>|<tuple|-10ln|-6ln>>>>|<line|<point|-1.88812675670718|-1.26343718410795>|<point|1.84579275670718|1.24810518410795>>>>>
<paragraph|�9.4 Ex.
3><with|gr-mode|<tuple|group-edit|move>|gr-frame|<tuple|scale|1cm|<tuple|0.400002gw|0.499997gh>>|gr-geometry|<tuple|geometry|6.9cm|2.55cm|center>|gr-grid|<tuple|empty>|gr-as-visual-grid|off|gr-line-width|1ln|gr-color|blue|gr-line-arrows|none|gr-edit-grid|<tuple|empty>|<graphics|<with|color|blue|line-width|2ln|line-arrows|<tuple|<with|dash-style|none|<line|<tuple|-10ln|6ln>|<tuple|0ln|0ln>|<tuple|-10ln|-6ln>>>>|<line|<point|-2.51756|0.725013>|<point|0.46696|0.725013>>>|<text-at|<with|mode|math|150<rsup|\<circ\>>>|<point|0.078598|0.111175>|left|bottom>|<text-at|<with|mode|math|\|<vec|u>\|=6>|<point|-1.72059|0.809679>|left|bottom>|<text-at|<with|mode|math|\|<vec|v>\|=8>|<point|1.92011|0.111176>|left|bottom>|<with|color|blue|<arc|<point|0.03626508|0.725014>|<point|0.417268|0.407512>|<point|0.777104|0.598013>>>|<with|color|blue|line-width|2ln|line-arrows|<tuple|<with|dash-style|none|<line|<tuple|-10ln|6ln>|<tuple|0ln|0ln>|<tuple|-10ln|-6ln>>>>|<line|<point|0.455296415214728|0.710538364275259>|<point|4.08345958478527|-0.97502395427526>>>>>
<hrule>
</body>
<\initial>
<\collection>
<associate|language|american>
<associate|par-hyphen|professional>
</collection>
</initial>
<\references>
<\collection>
<associate|auto-1|<tuple|1|?>>
<associate|auto-2|<tuple|2|?>>
<associate|footnote-1|<tuple|1|?>>
</collection>
</references>
<\auxiliary>
<\collection>
<\associate|toc>
<with|par-left|<quote|6fn>|9.4.2
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-1><vspace|0.15fn>>
<with|par-left|<quote|6fn>|9.4.3
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-2><vspace|0.15fn>>
</associate>
</collection>
</auxiliary>_______________________________________________
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