GraphingCalculator 4;
Window 49 7 849 1393;
PaneDivider 362;
FontSizes 18;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
3D.View 0.913147435323749 -0.07632735021628023 -0.4004196511205829 0.06398100575741046 0.9969747094317767 -0.04413456341940426 0.4025769395990472 0.01468211139157489 0.9152683996188027;
3D.Speed 0;
Text "Vector components relative to a basis in three dimensions.

Version 0.3 [4-1-15]
To do:
(i) Other bases?


Tip of the vector V and its components";
Color 7;
MathPaneSlider 36;
Expr a=slider([-5,5,40]);
Color 3;
MathPaneSlider 35;
Expr b=slider([-5,5,40]);
Color 5;
MathPaneSlider 36;
Expr c=slider([-5,5,40]);
Expr A=sqrt(a^2+b^2+c^2),T=acos([c/A]),P=atan([b/a]),L=sqrt(a^2+b^2);
Color 3;
Expr V=vector(a,b,c);
Color 6;
Expr R=slider([0,0.05]);
Color 17;
Grain 0.08333333333333333;
Expr V;
Color 2;
Expr O,V,'radius'=R;
Text "Unit vectors and origin:";
Color 4;
Expr I=vector(1,0,0),J=vector(0,1,0),K=vector(0,0,1),O=vector(0,0,0);
Color 17;
Expr O,I,'radius'=R;
Color 17;
Expr O,J,'radius'=R;
Color 17;
Expr O,K,'radius'=R;
Text "x, y, and z components:";
Color 17;
Expr O,a*I;
Color 17;
Expr O,b*J;
Color 17;
Expr O,c*K;
Text "Projection into x-y plane:";
Expr B=a*I+b*J;
Color 17;
Expr O,B,'radius'=R;
Color 17;
Expr B+t*c*K,'radius'=R;
Text "Perpendiculars:";
Color 17;
Expr a*I+t*b*J;
Color 17;
Expr b*J+t*a*I;
Color 17;
Expr c*K+t*B;
Text "V as a sum of its components in reference directions:";
Color 2;
Expr W=a*I+b*J+c*K;
Color 17;
Expr O,W,'radius'=R;
Text "Direction Cosines:";
Color 10;
Expr u*[V/A]+v*I,u^2+v^2<1;
Color 17;
Expr u*[V/A]+v*J,u^2+v^2<1;
Color 17;
Expr u*[V/A]+v*K,u^2+v^2<1;
Text "


<size=15>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>
";