GraphingCalculator 4;
Window 45 21 839 927;
PaneDivider 386;
FontSizes 18;
BackgroundType 0;
2D.BottomLeft -1.984375 -2.640625;
2D.GraphPaper 0;
2Dp.Scale 0.5 0.5 2 2;
2Dp.BottomLeft -4.78125 -1.75;
2Dp.GraphPaper 0;
Text "Scalar product of two vectors.   

Version 0.35 [2-6-14]
Note at some point along the line, GC decided it did not like the use of A,B as both subscripts labelling the lengths and angles L_a,b and T_a,b and also as names for the corresponding vectors.   For now it seems ok with using a,b, as labels, tbough.

To do:
(i) 3D? (no – begin with file 2vectors)


Tip of the vectors A, B and their components";
Color 7;
Expr a=2.8125+0.53125*i;
Color 5;
Expr b=-0.28125-(1.171875*i);
Expr L_a=abs(a),L_b=abs(b),C=abs(a)*abs(b);
Color 3;
Expr T_a=branch(if(atan([Im([a])/Re([a])]),Re([a])>0),if(atan([Im([a])/Re([a])])+pi,Re([a])<0));
Color 2;
Expr T_b=branch(if(atan([Im([b])/Re([b])]),Re([b])>0),if(atan([Im([b])/Re([b])])+pi,Re([b])<0));
Color 6;
Expr A_1=L_a*cos(T_a),A_2=L_a*sin(T_a),B_1=L_b*cos(T_b),B_2=L_b*sin(T_b);
Color 3;
Expr A=vector(A_1,A_2);
Color 4;
Expr B=vector(B_1,B_2);
Color 7;
Expr A;
Color 7;
Expr B;
Color 2;
Expr O,A;
Color 3;
Expr O,B;
Text "Unit vectors and origin:";
Color 4;
Expr A_h=A/L_a,B_h=B/L_b,O=vector(0,0);
Color 17;
Expr O,A_h;
Color 17;
Expr O,B_h;
Text "Scalar product plotted with vectors:";
Color 17;
Expr O,[dot(A,B)/L_b]*A_h;
Color 17;
Expr O,[dot(A,B)/L_a]*B_h;
Text "Perpendiculars:";
Color 17;
Expr dot(A,B)/L_b*B_h,A;
Color 17;
Expr dot(A,B)/L_a*A_h,B;
Color 8;
Expr vector(prime(x),prime(y))=vector(0,dot(A,B));
Color 8;
Expr abs(prime(y))=abs(a)*abs(b);
Text "Angle between A and B:";
Expr P=acos([dot(A_h,B_h)]);
Color 17;
Expr vector(prime(x),prime(y))=vector(P,dot(A,B));
Color 7;
Expr vector(prime(x),prime(y))=vector(P,dot(A,B)/(L_a*L_b));
Color 3;
Expr cos(prime(x));
Text "Shade angle between the vectors.   (Need to fix in 4th quadrant; something to do with definitions of angles Ta, Tb.)";
Color 7;
Expr min([T_a,T_b])<theta<min([T_a,T_b])+abs(T_a-T_b),r<1/2;
Color 7;
Expr min([T_a,T_b])<theta<min([T_a,T_b])+P,r<1/2;
Text "




<size=16>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";
Text "";