(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 21350, 530] NotebookOptionsPosition[ 20077, 482] NotebookOutlinePosition[ 20423, 497] CellTagsIndexPosition[ 20380, 494] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", RowBox[{"x", ",", "y", ",", "z", ",", "a", ",", "v", ",", "u", ",", "d"}], "]"}], ";"}]], "Input", CellChangeTimes->{{3.5719282973965654`*^9, 3.5719283170994005`*^9}, { 3.5719284697456684`*^9, 3.5719286303479505`*^9}, {3.5719290208322363`*^9, 3.5719291506400642`*^9}, {3.571934113943125*^9, 3.57193417947884*^9}, { 3.5719342298981285`*^9, 3.5719342453421555`*^9}, {3.5719348174575605`*^9, 3.5719348938040943`*^9}, 3.5719351866166086`*^9, {3.571981656213392*^9, 3.571981682390238*^9}, {3.571996093473087*^9, 3.57199609512669*^9}, { 3.571996595154368*^9, 3.5719966306132307`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"a", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "3", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "3", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1.5"}], "}"}]}], "}"}]}], "\[IndentingNewLine]", RowBox[{"MatrixForm", "[", "a", "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.5719282973965654`*^9, 3.5719283170994005`*^9}, { 3.5719284697456684`*^9, 3.5719286303479505`*^9}, {3.5719290208322363`*^9, 3.5719291506400642`*^9}, {3.571934113943125*^9, 3.57193417947884*^9}, { 3.5719342298981285`*^9, 3.5719342453421555`*^9}, {3.5719348174575605`*^9, 3.5719348938040943`*^9}, 3.5719351866166086`*^9, {3.571981656213392*^9, 3.571981682390238*^9}, {3.571996093473087*^9, 3.57199609512669*^9}, { 3.571996595154368*^9, 3.5719966306132307`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "3", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "3", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "1.5`"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{ 3.571997759431213*^9, 3.571997905104269*^9, 3.5719995063534813`*^9, 3.5719995557899685`*^9, {3.572011523113412*^9, 3.5720115512246614`*^9}, 3.5720116030011525`*^9, 3.572011636400811*^9, {3.57201167593128*^9, 3.572011700594924*^9}, {3.5720117430269985`*^9, 3.5720118530539913`*^9}, 3.5720161799975224`*^9, 3.5720171095719547`*^9, {3.572017177478874*^9, 3.5720172258077593`*^9}, 3.572017553361534*^9, 3.5720175906456*^9, { 3.572017665229331*^9, 3.57201768185896*^9}, 3.5720177502494802`*^9, { 3.5720178264712143`*^9, 3.572017851041257*^9}, 3.572017891913329*^9, 3.5720214028761463`*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "3", "1"}, {"1", "3", "0"}, {"1", "2", "1.5`"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.571997759431213*^9, 3.571997905104269*^9, 3.5719995063534813`*^9, 3.5719995557899685`*^9, {3.572011523113412*^9, 3.5720115512246614`*^9}, 3.5720116030011525`*^9, 3.572011636400811*^9, {3.57201167593128*^9, 3.572011700594924*^9}, {3.5720117430269985`*^9, 3.5720118530539913`*^9}, 3.5720161799975224`*^9, 3.5720171095719547`*^9, {3.572017177478874*^9, 3.5720172258077593`*^9}, 3.572017553361534*^9, 3.5720175906456*^9, { 3.572017665229331*^9, 3.57201768185896*^9}, 3.5720177502494802`*^9, { 3.5720178264712143`*^9, 3.572017851041257*^9}, 3.572017891913329*^9, 3.5720214028761463`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"v", "=", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}], "-", RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.5719282973965654`*^9, 3.5719283170994005`*^9}, { 3.5719284697456684`*^9, 3.5719286303479505`*^9}, {3.5719290208322363`*^9, 3.5719291506400642`*^9}, {3.571934113943125*^9, 3.57193417947884*^9}, { 3.5719342298981285`*^9, 3.5719342453421555`*^9}, {3.5719348174575605`*^9, 3.5719348938040943`*^9}, 3.5719351866166086`*^9, {3.571981656213392*^9, 3.571981682390238*^9}, {3.571996093473087*^9, 3.57199609512669*^9}, { 3.571996595154368*^9, 3.5719966306132307`*^9}, 3.5719968322435846`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{ 3.571997759431213*^9, 3.571997905104269*^9, 3.5719995063534813`*^9, 3.5719995557899685`*^9, {3.572011523129012*^9, 3.572011551240261*^9}, 3.5720116030167522`*^9, 3.572011636416411*^9, {3.5720116759468803`*^9, 3.5720117006105237`*^9}, {3.5720117430425987`*^9, 3.5720118530695915`*^9}, 3.572016180013122*^9, 3.572017109587555*^9, {3.572017177478874*^9, 3.572017225823359*^9}, 3.5720175533771343`*^9, 3.5720175906611996`*^9, { 3.5720176652449307`*^9, 3.5720176818745604`*^9}, 3.5720177502494802`*^9, { 3.572017826486814*^9, 3.572017851056857*^9}, 3.5720178919289293`*^9, 3.5720214028917465`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"u", "=", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "3", "]"}], "]"}], "-", RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}]}]}]], "Input", CellChangeTimes->{{3.5719282973965654`*^9, 3.5719283170994005`*^9}, { 3.5719284697456684`*^9, 3.5719286303479505`*^9}, {3.5719290208322363`*^9, 3.5719291506400642`*^9}, {3.571934113943125*^9, 3.57193417947884*^9}, { 3.5719342298981285`*^9, 3.5719342453421555`*^9}, {3.5719348174575605`*^9, 3.5719348938040943`*^9}, 3.5719351866166086`*^9, {3.571981656213392*^9, 3.571981682390238*^9}, {3.571996093473087*^9, 3.57199609512669*^9}, { 3.571996595154368*^9, 3.5719966306132307`*^9}, {3.5719968322435846`*^9, 3.571996851665619*^9}, {3.5719969837354507`*^9, 3.5719969842814517`*^9}, 3.5719971009384565`*^9, 3.5719975536356516`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}], ",", "1.5`"}], "}"}]], "Output", CellChangeTimes->{ 3.571997759446813*^9, 3.5719979051198688`*^9, 3.5719995063690815`*^9, 3.571999555805568*^9, {3.5720115231446123`*^9, 3.5720115512558613`*^9}, 3.5720116030167522`*^9, 3.572011636447611*^9, {3.5720116759468803`*^9, 3.5720117006105237`*^9}, {3.5720117430581985`*^9, 3.5720118530695915`*^9}, 3.5720161800287223`*^9, 3.572017109587555*^9, {3.572017177494474*^9, 3.572017225838959*^9}, 3.5720175533927345`*^9, 3.5720175906768*^9, { 3.5720176652449307`*^9, 3.57201768189016*^9}, 3.5720177502650805`*^9, { 3.572017826486814*^9, 3.572017851056857*^9}, 3.572017891944529*^9, 3.5720214029073467`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Plot1", "=", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"Opacity", "[", "0.5", "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}], ",", "0.1"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}], ",", "0.1"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "3", "]"}], "]"}], ",", "0.1"}], "]"}], ",", RowBox[{"Sphere", "[", RowBox[{"v", ",", "0.05"}], "]"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Plot2", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{"Text", "[", RowBox[{"i", ",", RowBox[{"a", "[", RowBox[{"[", "i", "]"}], "]"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "3"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Plot3", "=", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", ".05", "]"}], ",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], ",", "0.02"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"a", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", "0.02"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], ",", "0.02"}], "]"}]}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"Plot1", ",", "Plot2", ",", "Plot3", ",", RowBox[{"{", RowBox[{ RowBox[{"Axes", "\[Rule]", "Automatic"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", " ", RowBox[{"SphericalRegion", "\[Rule]", "True"}]}], "}"}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.5719282973965654`*^9, 3.5719283170994005`*^9}, { 3.5719284697456684`*^9, 3.5719286303479505`*^9}, {3.5719290208322363`*^9, 3.5719291506400642`*^9}, {3.571934113943125*^9, 3.57193417947884*^9}, { 3.5719342298981285`*^9, 3.5719342453421555`*^9}, {3.571934313311475*^9, 3.571934416053255*^9}, {3.5719345048954115`*^9, 3.5719345823807473`*^9}, { 3.5719346531736717`*^9, 3.5719346573856792`*^9}, {3.5719347433730297`*^9, 3.571934798690727*^9}, {3.5719349080937195`*^9, 3.571934928623356*^9}, { 3.5719350132535043`*^9, 3.571935119598891*^9}, {3.571976444618638*^9, 3.571976549232422*^9}, {3.5719765819144793`*^9, 3.571976602865316*^9}, 3.571981544329995*^9, {3.5719821819967155`*^9, 3.571982335719385*^9}, { 3.57198237832306*^9, 3.5719823916922836`*^9}, {3.571996886219679*^9, 3.5719969636894155`*^9}, {3.5719970320955353`*^9, 3.571997043249555*^9}}], Cell[BoxData[ Graphics3DBox[{ {Opacity[0.5], SphereBox[{2, 3, 1}, 0.1], SphereBox[{1, 3, 0}, 0.1], SphereBox[{1, 2, 1.5}, 0.1], SphereBox[{-1, 0, -1}, 0.05]}, Text3DBox["1", {2, 3, 1}, {1, 0}], Text3DBox["2", {1, 3, 0}, {1, 0}], Text3DBox["3", {1, 2, 1.5}, {1, 0}], {Arrowheads[0.05], Arrow3DBox[{{2, 3, 1}, {1, 3, 0}}, 0.02], Arrow3DBox[{{1, 3, 0}, {1, 2, 1.5}}, 0.02], Arrow3DBox[{{1, 2, 1.5}, {2, 3, 1}}, 0.02]}}, AspectRatio->Automatic, Axes->Automatic, AxesLabel->{ FormBox["x", TraditionalForm], FormBox["y", TraditionalForm], FormBox["z", TraditionalForm]}, PlotRange->Automatic, SphericalRegion->True]], "Output", CellChangeTimes->{ 3.5719977594624133`*^9, 3.5719979051354685`*^9, 3.5719995063846817`*^9, 3.571999555821168*^9, {3.5720115233942127`*^9, 3.5720115512714615`*^9}, 3.5720116030323524`*^9, 3.572011636463211*^9, {3.5720116759624805`*^9, 3.572011700626124*^9}, {3.572011743073798*^9, 3.5720118530851917`*^9}, 3.572016180044322*^9, 3.572017109603155*^9, {3.572017177510074*^9, 3.572017225854559*^9}, 3.5720175534083347`*^9, 3.5720175906924*^9, { 3.5720176652605305`*^9, 3.57201768189016*^9}, 3.57201775028068*^9, { 3.5720178265024137`*^9, 3.5720178510724573`*^9}, 3.572017891960129*^9, 3.572021402922947*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"d", "=", RowBox[{"Norm", "[", RowBox[{ RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}], "-", RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.5719960498398104`*^9, 3.5719960630218334`*^9}, { 3.571996117590729*^9, 3.5719961266543455`*^9}, {3.5720161717919073`*^9, 3.5720161729931097`*^9}}], Cell[BoxData[ SqrtBox["2"]], "Output", CellChangeTimes->{ 3.5719977594936132`*^9, 3.571997905182269*^9, 3.571999506462682*^9, 3.5719995558679686`*^9, {3.572011523472213*^9, 3.572011551302662*^9}, 3.5720116031103525`*^9, 3.572011636510011*^9, {3.572011676056081*^9, 3.572011700672924*^9}, {3.5720117431517982`*^9, 3.5720118531319914`*^9}, 3.5720161800911226`*^9, 3.5720171096967554`*^9, {3.5720171775568743`*^9, 3.572017225901359*^9}, 3.572017553439534*^9, 3.5720175907236*^9, { 3.572017665307331*^9, 3.57201768193696*^9}, 3.57201775031188*^9, { 3.572017826549214*^9, 3.572017851119257*^9}, 3.572017891991329*^9, 3.572021403000947*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"a", "[", RowBox[{"[", "1", "]"}], "]"}], ".", RowBox[{"a", "[", RowBox[{"[", "2", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.571997113621279*^9, 3.571997150686944*^9}, 3.5719976782330704`*^9, {3.571997747590792*^9, 3.571997753721603*^9}, { 3.5719994507861834`*^9, 3.571999479349834*^9}}], Cell[BoxData["11"], "Output", CellChangeTimes->{ 3.5719977595092134`*^9, 3.5719979051978693`*^9, 3.5719995064938817`*^9, 3.5719995558835683`*^9, {3.5720115235034127`*^9, 3.5720115513338614`*^9}, 3.5720116031259527`*^9, 3.572011636525611*^9, {3.5720116760872808`*^9, 3.5720117006885242`*^9}, {3.5720117431829987`*^9, 3.5720118531475916`*^9}, 3.5720161801379223`*^9, 3.572017109712355*^9, {3.5720171775568743`*^9, 3.5720172259169593`*^9}, 3.5720175534551344`*^9, 3.5720175907392*^9, { 3.572017665338531*^9, 3.5720176819525604`*^9}, 3.5720177503274803`*^9, { 3.572017826549214*^9, 3.572017851119257*^9}, 3.5720178920069294`*^9, 3.572021403000947*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"w", "=", RowBox[{"u", "\[Times]", "v"}]}], "\[IndentingNewLine]", RowBox[{"w", "=", RowBox[{"u", ".", "v"}]}]}], "Input", CellChangeTimes->{{3.571997690588292*^9, 3.5719977288551593`*^9}, { 3.5719978007088857`*^9, 3.5719978017540874`*^9}, {3.5719994912994547`*^9, 3.571999500409871*^9}, {3.571999540907542*^9, 3.571999547755954*^9}, { 3.572011511304191*^9, 3.5720115162026*^9}, 3.5720115465758533`*^9, { 3.572011582799117*^9, 3.572011594514737*^9}, {3.572011631486802*^9, 3.5720116316584024`*^9}, {3.5720116723744745`*^9, 3.572011695103714*^9}, { 3.57201173833139*^9, 3.5720118484051833`*^9}, {3.5720170815231056`*^9, 3.572017095906331*^9}, {3.572017132597595*^9, 3.5720172205505495`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", "0", ",", RowBox[{"-", "1.5`"}]}], "}"}]], "Output", CellChangeTimes->{ 3.5719995558991685`*^9, {3.5720115242678137`*^9, 3.5720115513494616`*^9}, 3.572011603141553*^9, 3.572011636541211*^9, {3.5720116760872808`*^9, 3.572011700704124*^9}, {3.572011743198599*^9, 3.572011853163192*^9}, 3.5720161801691227`*^9, 3.572017109727955*^9, {3.5720171775724745`*^9, 3.572017225932559*^9}, 3.5720175534707346`*^9, 3.5720175907392*^9, { 3.572017665338531*^9, 3.57201768196816*^9}, 3.5720177503430805`*^9, { 3.572017826564814*^9, 3.572017851134857*^9}, 3.572017892022529*^9, 3.5720214030165467`*^9}], Cell[BoxData[ RowBox[{"-", "1.5`"}]], "Output", CellChangeTimes->{ 3.5719995558991685`*^9, {3.5720115242678137`*^9, 3.5720115513494616`*^9}, 3.572011603141553*^9, 3.572011636541211*^9, {3.5720116760872808`*^9, 3.572011700704124*^9}, {3.572011743198599*^9, 3.572011853163192*^9}, 3.5720161801691227`*^9, 3.572017109727955*^9, {3.5720171775724745`*^9, 3.572017225932559*^9}, 3.5720175534707346`*^9, 3.5720175907392*^9, { 3.572017665338531*^9, 3.57201768196816*^9}, 3.5720177503430805`*^9, { 3.572017826564814*^9, 3.572017851134857*^9}, 3.572017892022529*^9, 3.5720214030165467`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Plot4", "=", RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", ".05", "]"}], ",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", "w", "}"}], ",", "0.02"}], "]"}]}], RowBox[{"(*", RowBox[{",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"w", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"w", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}], ",", "0.02"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"w", "[", RowBox[{"[", "3", "]"}], "]"}], ",", RowBox[{"w", "[", RowBox[{"[", "1", "]"}], "]"}]}], "}"}], ",", "0.02"}]}]}], "*)"}], "}"}], "]"}]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.5719978406293554`*^9, 3.571997873451813*^9}, { 3.572017492927028*^9, 3.57201758504519*^9}, {3.5720176587553196`*^9, 3.5720176751509485`*^9}, 3.5720177455226717`*^9, {3.5720178158787956`*^9, 3.5720178857825184`*^9}, 3.5720213954193335`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Show", "[", RowBox[{"Plot1", ",", "Plot2", ",", "Plot3", ",", "Plot4", ",", RowBox[{"{", RowBox[{ RowBox[{"Axes", "\[Rule]", "Automatic"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", " ", RowBox[{"SphericalRegion", "\[Rule]", "True"}]}], "}"}]}], "]"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.571997895011051*^9, 3.5719978980686564`*^9}}], Cell[BoxData[ Graphics3DBox[{ {Opacity[0.5], SphereBox[{2, 3, 1}, 0.1], SphereBox[{1, 3, 0}, 0.1], SphereBox[{1, 2, 1.5}, 0.1], SphereBox[{-1, 0, -1}, 0.05]}, Text3DBox["1", {2, 3, 1}, {1, 0}], Text3DBox["2", {1, 3, 0}, {1, 0}], Text3DBox["3", {1, 2, 1.5}, {1, 0}], {Arrowheads[0.05], Arrow3DBox[{{2, 3, 1}, {1, 3, 0}}, 0.02], Arrow3DBox[{{1, 3, 0}, {1, 2, 1.5}}, 0.02], Arrow3DBox[{{1, 2, 1.5}, {2, 3, 1}}, 0.02]}, {Arrowheads[0.05], Arrow3DBox[{-1.5}, 0.02]}}, AspectRatio->Automatic, AutomaticImageSize->True, Axes->Automatic, AxesLabel->{ FormBox["x", TraditionalForm], FormBox["y", TraditionalForm], FormBox["z", TraditionalForm]}, ImageSize->{360., 370.11022865089234`}, PlotRange->Automatic, SphericalRegion->True, ViewPoint->{2.7291316598673188`, -0.1754907927664755, 1.992747692198905}, ViewVertical->{ 0.9200690800271534, -0.2824413105135468, -0.35299522657078025`}]], "Output", CellChangeTimes->{ 3.571997905229069*^9, 3.571999506665482*^9, 3.571999555914768*^9, { 3.5720115247826147`*^9, 3.5720115513962617`*^9}, 3.5720116031571527`*^9, 3.5720116365568113`*^9, {3.5720116761184807`*^9, 3.5720117007197237`*^9}, { 3.5720117432141986`*^9, 3.572011853178792*^9}, 3.5720161801847224`*^9, 3.572017109743555*^9, {3.5720171775880747`*^9, 3.57201722613536*^9}, 3.572017553720335*^9, 3.5720175907548*^9, {3.572017665369731*^9, 3.572017682202161*^9}, 3.5720177503586807`*^9, {3.5720178265804143`*^9, 3.5720178511504574`*^9}, 3.572017892038129*^9, 3.5720214030321465`*^9}] }, Open ]] }, WindowSize->{707, 954}, WindowMargins->{{451, Automatic}, {Automatic, -12}}, FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (January 25, 2013)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[557, 20, 656, 11, 31, "Input"], Cell[CellGroupData[{ Cell[1238, 35, 886, 18, 72, "Input"], Cell[2127, 55, 900, 18, 31, "Output"], Cell[3030, 75, 1257, 28, 72, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4324, 108, 706, 13, 31, "Input"], Cell[5033, 123, 766, 14, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5836, 142, 836, 15, 31, "Input"], Cell[6675, 159, 747, 13, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7459, 177, 3568, 90, 192, "Input"], Cell[11030, 269, 1313, 26, 382, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12380, 300, 390, 10, 31, "Input"], Cell[12773, 312, 668, 11, 34, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13478, 328, 345, 8, 31, "Input"], Cell[13826, 338, 680, 10, 31, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14543, 353, 747, 12, 52, "Input"], Cell[15293, 367, 667, 12, 31, "Output"], Cell[15963, 381, 610, 10, 31, "Output"] }, Open ]], Cell[16588, 394, 1251, 34, 72, "Input"], Cell[CellGroupData[{ Cell[17864, 432, 622, 14, 92, "Input"], Cell[18489, 448, 1572, 31, 417, "Output"] }, Open ]] } ] *) (* End of internal cache information *)