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       "\!\(\*SubscriptBox[\(a\), \(1\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2102$$], 10, 
       "\!\(\*SubscriptBox[\(a\), \(2\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2103$$], 8, 
       "\!\(\*SubscriptBox[\(a\), \(3\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2104$$], -10, 
       "\!\(\*SubscriptBox[\(b\), \(1\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2105$$], -10, 
       "\!\(\*SubscriptBox[\(b\), \(2\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2106$$], 6, 
       "\!\(\*SubscriptBox[\(b\), \(3\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2107$$], -10, 
       "\!\(\*SubscriptBox[\(c\), \(1\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2108$$], 10, 
       "\!\(\*SubscriptBox[\(c\), \(2\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2109$$], -9, 
       "\!\(\*SubscriptBox[\(c\), \(3\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2110$$], 10, 
       "\!\(\*SubscriptBox[\(d\), \(1\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2111$$], -10, 
       "\!\(\*SubscriptBox[\(d\), \(2\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2112$$], -7, 
       "\!\(\*SubscriptBox[\(d\), \(3\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2113$$], 1, 
       "\!\(\*SubscriptBox[\(e\), \(1\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2114$$], 2, 
       "\!\(\*SubscriptBox[\(e\), \(2\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`$2115$$], 1, 
       "\!\(\*SubscriptBox[\(e\), \(3\)]\)"}, -10, 10, 1}, {{
       Hold[$CellContext`showP$$], True, "show P"}, {True, False}}, {{
       Hold[$CellContext`showText$$], True, "show Text"}, {True, False}}}, 
    Typeset`size$$ = {360., {200., 205.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`$2101$119631$$ = 0, $CellContext`$2102$119632$$ = 
    0, $CellContext`$2103$119633$$ = 0, $CellContext`$2104$119634$$ = 
    0, $CellContext`$2105$119635$$ = 0, $CellContext`$2106$119636$$ = 
    0, $CellContext`$2107$119637$$ = 0, $CellContext`$2108$119638$$ = 
    0, $CellContext`$2109$119639$$ = 0, $CellContext`$2110$119640$$ = 
    0, $CellContext`showP$119641$$ = False, $CellContext`showText$119642$$ = 
    False}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`showP$$ = True, $CellContext`showText$$ = 
        True, $CellContext`$2101$$ = 10, $CellContext`$2102$$ = 
        10, $CellContext`$2103$$ = 
        8, $CellContext`$2104$$ = -10, $CellContext`$2105$$ = -10, \
$CellContext`$2106$$ = 6, $CellContext`$2107$$ = -10, $CellContext`$2108$$ = 
        10, $CellContext`$2109$$ = -9, $CellContext`$2110$$ = 
        10, $CellContext`$2111$$ = -10, $CellContext`$2112$$ = -7, \
$CellContext`$2113$$ = 1, $CellContext`$2114$$ = 2, $CellContext`$2115$$ = 1},
       "ControllerVariables" :> {
        Hold[$CellContext`$2101$$, $CellContext`$2101$119631$$, 0], 
        Hold[$CellContext`$2102$$, $CellContext`$2102$119632$$, 0], 
        Hold[$CellContext`$2103$$, $CellContext`$2103$119633$$, 0], 
        Hold[$CellContext`$2104$$, $CellContext`$2104$119634$$, 0], 
        Hold[$CellContext`$2105$$, $CellContext`$2105$119635$$, 0], 
        Hold[$CellContext`$2106$$, $CellContext`$2106$119636$$, 0], 
        Hold[$CellContext`$2107$$, $CellContext`$2107$119637$$, 0], 
        Hold[$CellContext`$2108$$, $CellContext`$2108$119638$$, 0], 
        Hold[$CellContext`$2109$$, $CellContext`$2109$119639$$, 0], 
        Hold[$CellContext`$2110$$, $CellContext`$2110$119640$$, 0], 
        Hold[$CellContext`showP$$, $CellContext`showP$119641$$, False], 
        Hold[$CellContext`showText$$, $CellContext`showText$119642$$, False]},
       "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`ptA = {$CellContext`$2101$$, \
$CellContext`$2102$$, $CellContext`$2103$$}; $CellContext`ptB = \
{$CellContext`$2104$$, $CellContext`$2105$$, $CellContext`$2106$$}; \
$CellContext`ptC = {$CellContext`$2107$$, $CellContext`$2108$$, \
$CellContext`$2109$$}; $CellContext`ptD = {$CellContext`$2110$$, \
$CellContext`$2111$$, $CellContext`$2112$$}; $CellContext`ptE = \
{$CellContext`$2113$$, $CellContext`$2114$$, $CellContext`$2115$$}; 
       Subscript[$CellContext`n, 
          1] = ($CellContext`$2105$$ - $CellContext`$2102$$) \
($CellContext`$2112$$ - $CellContext`$2109$$) - ($CellContext`$2106$$ - \
$CellContext`$2103$$) ($CellContext`$2111$$ - $CellContext`$2108$$); 
       Subscript[$CellContext`n, 
          2] = ($CellContext`$2106$$ - $CellContext`$2103$$) \
($CellContext`$2110$$ - $CellContext`$2107$$) - ($CellContext`$2112$$ - \
$CellContext`$2109$$) ($CellContext`$2104$$ - $CellContext`$2101$$); 
       Subscript[$CellContext`n, 
          3] = ($CellContext`$2104$$ - $CellContext`$2101$$) \
($CellContext`$2111$$ - $CellContext`$2108$$) - ($CellContext`$2105$$ - \
$CellContext`$2102$$) ($CellContext`$2110$$ - $CellContext`$2107$$); \
$CellContext`solveACE = 
        Solve[{
          Subscript[$CellContext`n, 
               1] ($CellContext`x - $CellContext`$2113$$) + 
            Subscript[$CellContext`n, 
               2] ($CellContext`y - $CellContext`$2114$$) + 
            Subscript[$CellContext`n, 
               3] ($CellContext`z - $CellContext`$2115$$) == 
           0, $CellContext`x == $CellContext`$2101$$ + ($CellContext`$2107$$ - \
$CellContext`$2101$$) $CellContext`t, $CellContext`y == $CellContext`$2102$$ + \
($CellContext`$2108$$ - $CellContext`$2102$$) $CellContext`t, $CellContext`z == \
$CellContext`$2103$$ + ($CellContext`$2109$$ - $CellContext`$2103$$) \
$CellContext`t}, {$CellContext`x, $CellContext`y, $CellContext`z, \
$CellContext`t}]; $CellContext`solveADE = 
        Solve[{Subscript[$CellContext`n, 
               1] ($CellContext`x - $CellContext`$2113$$) + 
            Subscript[$CellContext`n, 
               2] ($CellContext`y - $CellContext`$2114$$) + 
            Subscript[$CellContext`n, 
               3] ($CellContext`z - $CellContext`$2115$$) == 
           0, $CellContext`x == $CellContext`$2101$$ + ($CellContext`$2110$$ - \
$CellContext`$2101$$) $CellContext`t, $CellContext`y == $CellContext`$2102$$ + \
($CellContext`$2111$$ - $CellContext`$2102$$) $CellContext`t, $CellContext`z == \
$CellContext`$2103$$ + ($CellContext`$2112$$ - $CellContext`$2103$$) \
$CellContext`t}, {$CellContext`x, $CellContext`y, $CellContext`z, \
$CellContext`t}]; $CellContext`solveBCE = 
        Solve[{Subscript[$CellContext`n, 
               1] ($CellContext`x - $CellContext`$2113$$) + 
            Subscript[$CellContext`n, 
               2] ($CellContext`y - $CellContext`$2114$$) + 
            Subscript[$CellContext`n, 
               3] ($CellContext`z - $CellContext`$2115$$) == 
           0, $CellContext`x == $CellContext`$2104$$ + ($CellContext`$2107$$ - \
$CellContext`$2104$$) $CellContext`t, $CellContext`y == $CellContext`$2105$$ + \
($CellContext`$2108$$ - $CellContext`$2105$$) $CellContext`t, $CellContext`z == \
$CellContext`$2106$$ + ($CellContext`$2109$$ - $CellContext`$2106$$) \
$CellContext`t}, {$CellContext`x, $CellContext`y, $CellContext`z, \
$CellContext`t}]; $CellContext`solveBDE = 
        Solve[{
          Subscript[$CellContext`n, 
               1] ($CellContext`x - $CellContext`$2113$$) + 
            Subscript[$CellContext`n, 
               2] ($CellContext`y - $CellContext`$2114$$) + 
            Subscript[$CellContext`n, 
               3] ($CellContext`z - $CellContext`$2115$$) == 
           0, $CellContext`x == $CellContext`$2104$$ + ($CellContext`$2110$$ - \
$CellContext`$2104$$) $CellContext`t, $CellContext`y == $CellContext`$2105$$ + \
($CellContext`$2111$$ - $CellContext`$2105$$) $CellContext`t, $CellContext`z == \
$CellContext`$2106$$ + ($CellContext`$2112$$ - $CellContext`$2106$$) \
$CellContext`t}, {$CellContext`x, $CellContext`y, $CellContext`z, \
$CellContext`t}]; $CellContext`ptP = 
        ReplaceAll[{$CellContext`x, $CellContext`y, $CellContext`z}, 
          Part[$CellContext`solveACE, 1]]; $CellContext`ptQ = 
        ReplaceAll[{$CellContext`x, $CellContext`y, $CellContext`z}, 
          Part[$CellContext`solveADE, 1]]; $CellContext`ptR = 
        ReplaceAll[{$CellContext`x, $CellContext`y, $CellContext`z}, 
          Part[$CellContext`solveBCE, 1]]; $CellContext`ptS = 
        ReplaceAll[{$CellContext`x, $CellContext`y, $CellContext`z}, 
          Part[$CellContext`solveBDE, 1]]; 
       If[$CellContext`showText$$, {$CellContext`showP$$ = True}, {}]; Show[
         ContourPlot3D[
         Subscript[$CellContext`n, 1] ($CellContext`x - $CellContext`$2113$$) + 
           Subscript[$CellContext`n, 
              2] ($CellContext`y - $CellContext`$2114$$) + 
           Subscript[$CellContext`n, 
              3] ($CellContext`z - $CellContext`$2115$$) == 
          0, {$CellContext`x, -10, 10}, {$CellContext`y, -10, 
           10}, {$CellContext`z, -10, 10}, Axes -> True, 
          AxesLabel -> {$CellContext`x, $CellContext`y, $CellContext`z}, Mesh -> 
          None, ContourStyle -> Directive[Blue, 
            Opacity[0.2]]], 
         Graphics3D[{PointSize -> 0.01, Blue, 
           Point[$CellContext`ptA]}], 
         Graphics3D[{PointSize -> 0.01, Blue, 
           Point[$CellContext`ptB]}], 
         Graphics3D[{PointSize -> 0.01, Blue, 
           Point[$CellContext`ptC]}], 
         Graphics3D[{PointSize -> 0.01, Blue, 
           Point[$CellContext`ptD]}], 
         Graphics3D[
          If[$CellContext`showP$$, {PointSize -> 0.01, Blue, 
            
            Point[{$CellContext`$2113$$, $CellContext`$2114$$, \
$CellContext`$2115$$}]}, {}]], 
         Graphics3D[
          If[$CellContext`showText$$, {
            Text[
             Style[
              StringForm[
              "E( ``,``,`` )", $CellContext`$2113$$, $CellContext`$2114$$, \
$CellContext`$2115$$, 16, Blue]], {$CellContext`$2113$$ + 
              1, $CellContext`$2114$$ + 1, $CellContext`$2115$$ + 1}]}, {}]], 
         
         ParametricPlot3D[{$CellContext`$2101$$ + ($CellContext`$2104$$ - \
$CellContext`$2101$$) $CellContext`t, $CellContext`$2102$$ + \
($CellContext`$2105$$ - $CellContext`$2102$$) $CellContext`t, \
$CellContext`$2103$$ + ($CellContext`$2106$$ - $CellContext`$2103$$) \
$CellContext`t}, {$CellContext`t, -3, 3}, PlotStyle -> Directive[Red, Thick]],
          
         ParametricPlot3D[{$CellContext`$2107$$ + ($CellContext`$2110$$ - \
$CellContext`$2107$$) $CellContext`t, $CellContext`$2108$$ + \
($CellContext`$2111$$ - $CellContext`$2108$$) $CellContext`t, \
$CellContext`$2109$$ + ($CellContext`$2112$$ - $CellContext`$2109$$) \
$CellContext`t}, {$CellContext`t, -3, 3}, PlotStyle -> 
          Directive[Blue, Thick]], 
         Graphics3D[{Thick, Green, 
           Line[{$CellContext`ptA, $CellContext`ptC}]}], 
         Graphics3D[{Thick, Green, 
           Line[{$CellContext`ptA, $CellContext`ptD}]}], 
         Graphics3D[{Thick, Green, 
           Line[{$CellContext`ptB, $CellContext`ptC}]}], 
         Graphics3D[{Thick, Green, 
           Line[{$CellContext`ptB, $CellContext`ptD}]}], 
         Graphics3D[{PointSize -> 0.04, Blue, 
           Point[$CellContext`ptP]}], 
         Graphics3D[{PointSize -> 0.04, Blue, 
           Point[$CellContext`ptQ]}], 
         Graphics3D[{PointSize -> 0.04, Blue, 
           Point[$CellContext`ptR]}], 
         Graphics3D[{PointSize -> 0.04, Blue, 
           Point[$CellContext`ptS]}], 
         Graphics3D[{Thick, Blue, Dashed, 
           Line[{$CellContext`ptP, $CellContext`ptQ}]}], 
         Graphics3D[{Thick, Red, Dashed, 
           Line[{$CellContext`ptQ, $CellContext`ptS}]}], 
         Graphics3D[{Thick, Blue, Dashed, 
           Line[{$CellContext`ptS, $CellContext`ptR}]}], 
         Graphics3D[{Thick, Red, Dashed, 
           Line[{$CellContext`ptR, $CellContext`ptP}]}]]), 
      "Specifications" :> {{{$CellContext`$2101$$, 10, 
          "\!\(\*SubscriptBox[\(a\), \(1\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2102$$, 10, 
          "\!\(\*SubscriptBox[\(a\), \(2\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2103$$, 8, 
          "\!\(\*SubscriptBox[\(a\), \(3\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> Small}, 
        Delimiter, {{$CellContext`$2104$$, -10, 
          "\!\(\*SubscriptBox[\(b\), \(1\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2105$$, -10, 
          "\!\(\*SubscriptBox[\(b\), \(2\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2106$$, 6, 
          "\!\(\*SubscriptBox[\(b\), \(3\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> Small}, 
        Delimiter, {{$CellContext`$2107$$, -10, 
          "\!\(\*SubscriptBox[\(c\), \(1\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2108$$, 10, 
          "\!\(\*SubscriptBox[\(c\), \(2\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2109$$, -9, 
          "\!\(\*SubscriptBox[\(c\), \(3\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> Small}, 
        Delimiter, {{$CellContext`$2110$$, 10, 
          "\!\(\*SubscriptBox[\(d\), \(1\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2111$$, -10, 
          "\!\(\*SubscriptBox[\(d\), \(2\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2112$$, -7, 
          "\!\(\*SubscriptBox[\(d\), \(3\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> Small}, 
        Delimiter, {{$CellContext`$2113$$, 1, 
          "\!\(\*SubscriptBox[\(e\), \(1\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2114$$, 2, 
          "\!\(\*SubscriptBox[\(e\), \(2\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`$2115$$, 1, 
          "\!\(\*SubscriptBox[\(e\), \(3\)]\)"}, -10, 10, 1, Appearance -> 
         "Labeled", ImageSize -> 
         Small}, {{$CellContext`showP$$, True, "show P"}, {
         True, False}}, {{$CellContext`showText$$, True, "show Text"}, {
         True, False}}}, "Options" :> {ControlPlacement -> Left}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{611., {226., 231.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`ptA = {10, 10, 
        8}, $CellContext`ptB = {-10, -10, 6}, $CellContext`ptC = {-10, 
        10, -9}, $CellContext`ptD = {10, -10, -7}, $CellContext`ptE = {1, 2, 
        1}, Attributes[Subscript] = {NHoldRest}, 
       Subscript[$CellContext`a, 3] = -1, Subscript[$CellContext`b, 3] = 12, 
       Subscript[$CellContext`c, 3] = 14, Subscript[$CellContext`n, 1] = -80, 
       Subscript[$CellContext`n, 2] = 0, Subscript[$CellContext`n, 3] = 800, 
       Subscript[{163/150}, 1] = -80, Subscript[{163/150}, 2] = 0, 
       Subscript[{163/150}, 3] = 
       800, $CellContext`n = {
        163/150}, $CellContext`solveACE = {{$CellContext`x -> 
          28/15, $CellContext`y -> 10, $CellContext`z -> 
          163/150, $CellContext`t -> 
          61/150}}, $CellContext`solveADE = {{$CellContext`x -> 
          10, $CellContext`y -> 28/15, $CellContext`z -> 
          19/10, $CellContext`t -> 
          61/150}}, $CellContext`solveBCE = {{$CellContext`x -> -10, \
$CellContext`y -> (-28)/15, $CellContext`z -> (-1)/10, $CellContext`t -> 
          61/150}}, $CellContext`solveBDE = {{$CellContext`x -> (-28)/
           15, $CellContext`y -> -10, $CellContext`z -> 
          107/150, $CellContext`t -> 61/150}}, $CellContext`ptP = {
        28/15, 10, 163/150}, $CellContext`ptQ = {
        10, 28/15, 19/10}, $CellContext`ptR = {-10, (-28)/15, (-1)/
         10}, $CellContext`ptS = {(-28)/15, -10, 107/150}}; 
     Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.434428714109375*^9, 3.4344287881875*^9, {3.434428879890625*^9, 
   3.43442890684375*^9}, 3.4344289650625*^9, {3.43442913725*^9, 
   3.434429147453125*^9}, 3.434429210046875*^9, 3.434429241390625*^9}]
}, Open  ]]
},
WindowSize->{1016, 666},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
Magnification->1.,
FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (February 7, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 59142, 1637, 1412, "Input"],
Cell[59735, 1662, 17509, 318, 474, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)