GraphingCalculator 4;
Window 49 7 829 1270;
PaneDivider 388;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
2D.Scale 0.1 0.1 5 5;
2D.BottomLeft -0.39375 -0.71875;
2D.Axes 0;
2D.GraphPaper 0;
Text "Vector components relative to different bases.

Version 0.45 [4-1-15]
To do:
(i) ?


Tip of the vector V and its components";
Color 7;
Expr a=1.46875+1.0625*i;
Expr A=abs(a);
Color 3;
Expr T=branch(if(atan([Im([a])/Re([a])]),Re([a])>0),if(atan([Im([a])/Re([a])])+pi,Re([a])<0));
Color 6;
Expr A_1=A*cos(T),A_2=A*sin(T);
Color 3;
Expr V=vector(A_1,A_2);
Color 2;
Expr O,V;
Text "Unit vectors and origin:";
Color 4;
Expr I=vector(1,0),J=vector(0,1),O=vector(0,0);
Color 17;
Expr O,I;
Color 17;
Expr O,J;
Text "x and y components:";
Color 17;
Expr O,A_1*I;
Color 17;
Expr O,A_2*J;
Text "Perpendiculars:";
Color 17;
Expr A_1*I+t*A_2*J;
Color 17;
Expr A_2*J+t*A_1*I;
Text "V as a sum of its components in reference directions:";
Color 2;
Expr W=A_1*I+A_2*J;
Color 17;
Expr O,W;
Text "Components relative to a rotated basis:";
Color 5;
Expr p=slider([0,1]);
Color 8;
Expr P=2*pi*p;
Expr M=vector(cos(P),sin(P)),N=vector(-sin(P),cos(P));
Color 17;
Expr O,M;
Color 17;
Expr O,N;
Color 4;
Expr b_1=A_1*cos(P)+A_2*sin(P),b_2=-(A_1*sin(P))+A_2*cos(P);
Color 5;
Expr B_1=dot(M,V),B_2=dot(N,V);
Color 17;
Expr O,B_1*M;
Color 17;
Expr O,B_2*N;
Text "Perpendiculars:";
Color 17;
Expr B_1*M+t*B_2*N;
Color 17;
Expr B_2*N+t*B_1*M;
Text "Rotated axes:";
Color 17;
Expr 20*t*M;
Color 17;
Expr 20*t*N;
Text "



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