toVect[v_]:=Module[{vec="⟨ ",n},
For[n=1,n≤Length[v],n++,
(vec=StringJoin[vec,ToString[#]])&[v[[n]]];
vec=StringJoin[vec,If[n≠Length[v],", "," ⟩"]];
];
Return[vec];
]
theu = {4,1};
thev = {2,3};
Manipulate[
Deploy[GraphicsRow[{Show[
{Graphics[Locator[Dynamic[theu]]],Graphics[Locator[Dynamic[thev]]],
Graphics[{Thickness[.003],Arrow[{{0,0},Dynamic[theu]}],Text[Style[OverVector["u"],25],Dynamic[theu],{-1,-1}]}],Graphics[{Thickness[.003],Arrow[{{0,0},Dynamic[thev]}],Text[Style[OverVector["v"],25],Dynamic[thev],{-1,-1}]}],If[theta,Graphics[Text[Style["θ",15],Dynamic[(1/2)((thev/(Norm[thev]))+(theu/(Norm[theu])))]]]],
If[units,Graphics[{Thickness[.004],Magenta,Arrow[{{0,0},Dynamic[(theu/(Norm[theu]))]}]}]],
If[units,Graphics[{Thickness[.004],Magenta,Arrow[{{0,0},Dynamic[(thev/(Norm[thev]))]}]}]],
If[para,Graphics[{Thickness[.004],Dotted,Line[{Dynamic[theu],Dynamic[theu+thev]}]}]],
If[para,Graphics[{Thickness[.004],Dotted,Line[{Dynamic[thev],Dynamic[theu+thev]}]}]]

}/.Null->Nothing
,AxesOrigin->{0,0},Axes->True,Ticks->{Range[-5,5],Range[-5,5]},PlotRange->8,ImageSize->300
],TableForm[{{Style["(Overscript[u, ->])",20],Style["=",20],Style[Dynamic[toVect[Round[theu,.1]]],20],Style["\[LeftBracketingBar](Overscript[u, ->])\[RightBracketingBar]",20],Style["=",20],Style[Dynamic[Round[Norm[theu],.1]],20]},{Style["(Overscript[v, ->])",20],Style["=",20],Style[Dynamic[toVect[Round[thev,.1]]],20],Style["\[LeftBracketingBar](Overscript[v, ->])\[RightBracketingBar]",20],Style["=",20],Style[Dynamic[Round[Norm[thev],.1]],20]},
{Style["θ",20],Style["=",20],Style[Dynamic[StringJoin[ToString[Round[ArcCos[((theu.thev)/(Norm[theu]Norm[thev]))]/Degree,.1]],"°"]],20]},
{Style["(Overscript[u, ->]).(Overscript[v, ->])",20],Style["=",20],Style[Dynamic[Round[theu.thev,.1]],20]},
{Style["\[LeftBracketingBar](Overscript[u, ->])\[Cross](Overscript[v, ->])\[RightBracketingBar]",20],Style["=",20],Style[Dynamic[Round[Norm[Cross[Append[theu,0],Append[thev,0]]],.1]],20]}
},TableSpacing->{0, 1}]},Spacings->10]],
{{theta,False,Style["Show θ",12]},{True,False}},
{{units,False,Style["Show unit vecs",12]},{True,False}},
{{para,False,Style["Show parallelogram",12]},{True,False}}
]