Your Assignment:
1) Execute the entire notebook. 
    Experiment if you like. 
2) Find the force and theta3 values. 
3) Hand in the plot.
4) (Optional): Use analytic methods to solve this problem.

Clear["Global`*"];

Initialization: 
(Don't read this; just execute it)
(Click on the outer bracket--far right--and hit the ENTER key.

Define the cross product:

Needs["LinearAlgebra`CrossProduct`"]

Off[ General::spell ];
Off[ General::spell1];

Clear["Global`*"];

VectorPlot[list__List?VectorQ]:= VectorPlot[{list}];

VectorPlot[list_List?MatrixQ]:= 
Module[{xlist,length,totList},
 xlist=Join[{{0,0}},list];
 length=Length[xlist];
 totList=Table[ Sum[ xlist[[i]] ,{i,1,j}],{j,1,length}];
 Return[
  Show[Graphics[{Thickness[0.015],Line[totList]}
          ,{GridLines->Automatic
           ,Axes->True}]]
 ]
];

VectorPlot3D[list__List?VectorQ]:= VectorPlot3D[{list}];

VectorPlot3D[list_List?MatrixQ]:= 
Module[{xlist,length,totList},
 xlist=Join[{{0,0,0}},list];
 length=Length[xlist];
 totList=Table[ Sum[ xlist[[i]] ,{i,1,j}],{j,1,length}];
 Return[
  Show[Graphics3D[{Thickness[0.015],Line[totList]}
          ,{ FaceGrids->{{0,0,-1},{0,1,0},{-1,0,0}}
            ,BoxRatios->{1,1,1}
            ,Axes->True}]]
 ]
];

VectorLength[vector_List?VectorQ]:=Sqrt[vector.vector]

Protect[{VectorPlot,VectorPlot3D,VectorLength}];
Off[Clear::wrsym];

2-Dimensional Tug of War

Three students play a 2-Dimensional version of Tug of War. Abe and Betty pull with known forces. Charlie pulls with an unknown force, but you do know that the system is at rest. Use this information to find the force with which Charlie pulls.

Abe's force is 14, and the angle is 33:

Clear["Global`*"];

Abe= 14 {Cos[33 Degree],Sin[33 Degree]}

Betty's force is 23, and the angle is -47:

Betty= 23 {Cos[-47 Degree],Sin[-47 Degree]}

Charlie's force is unknown. We will write it as:

Charlie= force {Cos[theta3 Degree],Sin[theta3 Degree]}

Plot these vectors, added head to toe.  By trial and error, try to find the force and angle for Charlie.

force=10;
theta3=45;
VectorPlot[Abe,Betty,Charlie];

To see numerically how well you did, let us compute the length of the total force vector.

force=10;
theta3=175;
VectorPlot[Abe,Betty,Charlie];

VectorLength[Abe+Betty+Charlie] //N