Example 6.1.2

This notebook shows a geometric interpretation of vector addition given in example 6.1.2.  Given vectors (OverVector[v]) and (OverVector[w]) in "tail-to-tail" position, the vector (OverVector[v])+(OverVector[w]) is the diagonal of the parallelogram spanned by  (OverVector[v]) and (OverVector[w]) (that is, with  (OverVector[v]) and (OverVector[w]) as two of its sides).

ShowArrows[ pt1_, pt2_]:=Block[ {graphics},
graphics=Graphics[{Blue, Arrow[{{0,0},pt1}], Red, Arrow[ {{0,0},pt2}],Green, Arrow[ {{0,0}, pt1+pt2}], Black, Text["v",pt1/2,{1,1}],Text["w", pt2/2,{1,1}], Text["v+w", (pt1+pt2)/2],Opacity[.1], Red, Polygon[ {{0,0}, pt1, pt1+pt2,pt2}]}];
Return[ Show[graphics,PlotRange->{{-5,5},{-5,5}}, AxesOrigin->{0,0}, Axes->True]]
]

Manipulate[ShowArrows[pt1,pt2],{{pt1,{-2,2}},Locator, Appearance->None}, {{pt2,{3,1}},Locator, Appearance->None}, SaveDefinitions->True]