(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 8123, 210] NotebookOptionsPosition[ 7747, 194] NotebookOutlinePosition[ 8093, 209] CellTagsIndexPosition[ 8050, 206] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[{ RowBox[{ RowBox[{"Needs", "[", "\"\\"", "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["u", FontColor->RGBColor[0, 1, 0]], "=", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ StyleBox["v", FontColor->RGBColor[0, 0, 1]], "=", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", "5", ",", "7"}], "}"}]}], ";"}], "\n", RowBox[{"DotProduct", "[", RowBox[{"u", ",", "v"}], "]"}], "\[IndentingNewLine]", RowBox[{"u", ".", "v"}]}], "Input", CellChangeTimes->{ 3.396644788671875*^9, {3.396644828390625*^9, 3.3966448290625*^9}, 3.41036320778125*^9, {3.466109573546875*^9, 3.466109576703125*^9}, { 3.470154766703125*^9, 3.470154771484375*^9}, {3.47015482040625*^9, 3.470154859703125*^9}, {3.4701549219375*^9, 3.47015494659375*^9}, { 3.470155028453125*^9, 3.470155031515625*^9}, {3.47015513590625*^9, 3.470155142125*^9}, {3.47015518665625*^9, 3.47015522803125*^9}, { 3.470169616796875*^9, 3.47016977259375*^9}, {3.470169812671875*^9, 3.47016983246875*^9}, {3.470244899578125*^9, 3.47024495790625*^9}, { 3.470245004015625*^9, 3.470245094265625*^9}, 3.471194447234375*^9}], Cell[BoxData[ RowBox[{ RowBox[{"v", ".", "u"}], "-", RowBox[{"u", ".", "v"}]}]], "Input", CellChangeTimes->{ 3.396644788671875*^9, {3.396644828390625*^9, 3.3966448290625*^9}, 3.41036320778125*^9, {3.466109573546875*^9, 3.466109576703125*^9}, { 3.470154766703125*^9, 3.470154771484375*^9}, {3.47015482040625*^9, 3.470154859703125*^9}, {3.4701549219375*^9, 3.47015494659375*^9}, { 3.470155028453125*^9, 3.470155031515625*^9}, {3.47015513590625*^9, 3.470155142125*^9}, {3.47015518665625*^9, 3.47015522803125*^9}, { 3.470169616796875*^9, 3.47016977259375*^9}, {3.470169812671875*^9, 3.47016983246875*^9}, {3.470244899578125*^9, 3.47024495790625*^9}, { 3.470245004015625*^9, 3.470245094265625*^9}, {3.471194447234375*^9, 3.47119445096875*^9}}], Cell[BoxData[{ RowBox[{"VectorAngle", "[", RowBox[{"u", ",", "v"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"VectorAngle", "[", RowBox[{"u", ",", "v"}], "]"}], "//", "N"}], "\n", RowBox[{"%", "*", FractionBox["180", "\[Pi]"]}], "\[IndentingNewLine]", RowBox[{"Framed", "@", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"PointSize", "[", "0.02", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{"Green", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "u"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "v"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"400", ",", "400"}], "}"}]}], ",", " ", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}]}], "Input", CellChangeTimes->{ 3.396644788671875*^9, {3.396644828390625*^9, 3.3966448290625*^9}, 3.41036320778125*^9, {3.466109573546875*^9, 3.466109576703125*^9}, { 3.470154766703125*^9, 3.470154771484375*^9}, {3.47015482040625*^9, 3.470154859703125*^9}, {3.4701549219375*^9, 3.47015494659375*^9}, { 3.470155028453125*^9, 3.470155031515625*^9}, {3.47015513590625*^9, 3.470155142125*^9}, {3.47015518665625*^9, 3.47015522803125*^9}, { 3.470169616796875*^9, 3.47016977259375*^9}, {3.470169812671875*^9, 3.47016983246875*^9}, {3.470244899578125*^9, 3.47024495790625*^9}, { 3.470245004015625*^9, 3.470245094265625*^9}, {3.471194447234375*^9, 3.471194470609375*^9}, {3.47277171290625*^9, 3.472771727671875*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"b", "=", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ StyleBox["w", FontColor->RGBColor[1, 0, 0]], "=", RowBox[{"Projection", "[", RowBox[{"v", ",", "b"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"Framed", "@", RowBox[{"Show", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Graphics3D", "[", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"PointSize", "[", "0.02", "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "b"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "v"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", " ", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", "w"}], "}"}], "]"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"{", RowBox[{"400", ",", "400"}], "}"}]}], ",", " ", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]}]}], "Input", CellChangeTimes->{ 3.396644788671875*^9, {3.396644828390625*^9, 3.3966448290625*^9}, 3.41036320778125*^9, {3.466109573546875*^9, 3.466109576703125*^9}, { 3.470154766703125*^9, 3.470154771484375*^9}, {3.47015482040625*^9, 3.470154859703125*^9}, {3.4701549219375*^9, 3.47015494659375*^9}, { 3.470155028453125*^9, 3.470155031515625*^9}, {3.47015513590625*^9, 3.470155142125*^9}, {3.47015518665625*^9, 3.47015522803125*^9}, { 3.470169616796875*^9, 3.47016977259375*^9}, {3.470169812671875*^9, 3.47016983246875*^9}, {3.470244899578125*^9, 3.47024495790625*^9}, { 3.470245004015625*^9, 3.470245094265625*^9}, {3.471194447234375*^9, 3.471194470609375*^9}, {3.47277178609375*^9, 3.472771863765625*^9}, { 3.47277190659375*^9, 3.472771913*^9}, {3.472771953015625*^9, 3.47277201909375*^9}}] }, WindowSize->{1146, 891}, WindowMargins->{{Automatic, 47}, {Automatic, 10}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 1251, 29, 112, "Input"], Cell[1799, 51, 779, 14, 31, "Input"], Cell[2581, 67, 2367, 55, 188, "Input"], Cell[4951, 124, 2792, 68, 172, "Input"] } ] *) (* End of internal cache information *)