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main.toc
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main.toc
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\vskip -8pt
\contentsline {schapter}{Introduction}{iii}{chapter*.2}%
\contentsline {chapter}{\numberline {1}Vectors}{1}{chapter.1}%
\contentsline {section}{\numberline {1.1}Length}{1}{section.1.1}%
\contentsline {section}{\numberline {1.2}Distance}{10}{section.1.2}%
\contentsline {section}{\numberline {1.3}Exercises}{19}{section.1.3}%
\contentsline {section}{\numberline {1.4}Section Formula}{22}{section.1.4}%
\contentsline {section}{\numberline {1.5}Exercises}{44}{section.1.5}%
\contentsline {section}{\numberline {1.6}Rank}{47}{section.1.6}%
\contentsline {section}{\numberline {1.7}Exercises}{60}{section.1.7}%
\contentsline {section}{\numberline {1.8}Scalar Product}{61}{section.1.8}%
\contentsline {section}{\numberline {1.9}Exercises}{75}{section.1.9}%
\contentsline {section}{\numberline {1.10}Orthogonality}{79}{section.1.10}%
\contentsline {section}{\numberline {1.11}Exercises}{110}{section.1.11}%
\contentsline {section}{\numberline {1.12}Vector Product}{115}{section.1.12}%
\contentsline {section}{\numberline {1.13}Exercises}{142}{section.1.13}%
\contentsline {section}{\numberline {1.14}Miscellaneous}{145}{section.1.14}%
\contentsline {section}{\numberline {1.15}Exercises}{163}{section.1.15}%
\contentsline {section}{\numberline {1.16}Triangle}{164}{section.1.16}%
\contentsline {section}{\numberline {1.17}Exercises}{174}{section.1.17}%
\contentsline {section}{\numberline {1.18} Quadrilateral}{182}{section.1.18}%
\contentsline {section}{\numberline {1.19}Exercises}{190}{section.1.19}%
\contentsline {chapter}{\numberline {2}Linear Forms}{205}{chapter.2}%
\contentsline {section}{\numberline {2.1}Equation of a Line}{205}{section.2.1}%
\contentsline {section}{\numberline {2.2}Perpendicular}{240}{section.2.2}%
\contentsline {section}{\numberline {2.3}Plane}{266}{section.2.3}%
\contentsline {section}{\numberline {2.4}Miscellaneous }{273}{section.2.4}%
\contentsline {section}{\numberline {2.5}Exemplar}{288}{section.2.5}%
\contentsline {section}{\numberline {2.6}Singular Value Decomposition}{301}{section.2.6}%
\contentsline {chapter}{\numberline {3}Conics}{323}{chapter.3}%
\contentsline {section}{\numberline {3.1}Circle}{323}{section.3.1}%
\contentsline {section}{\numberline {3.2}Exercises}{342}{section.3.2}%
\contentsline {section}{\numberline {3.3}Construction}{345}{section.3.3}%
\contentsline {section}{\numberline {3.4}Exercises}{382}{section.3.4}%
\contentsline {section}{\numberline {3.5}Parabola}{395}{section.3.5}%
\contentsline {section}{\numberline {3.6}Exercises}{416}{section.3.6}%
\contentsline {section}{\numberline {3.7}Ellipse}{418}{section.3.7}%
\contentsline {section}{\numberline {3.8}Exercises}{444}{section.3.8}%
\contentsline {section}{\numberline {3.9}Hyperbola}{446}{section.3.9}%
\contentsline {section}{\numberline {3.10}Exercises}{467}{section.3.10}%
\contentsline {chapter}{\numberline {4}Intersection of Conics}{527}{chapter.4}%
\contentsline {section}{\numberline {4.1}Chords }{527}{section.4.1}%
\contentsline {section}{\numberline {4.2}Curves}{555}{section.4.2}%
\contentsline {chapter}{\numberline {5}Tangent And Normal}{567}{chapter.5}%
\contentsline {section}{\numberline {5.1}Examples}{567}{section.5.1}%
\contentsline {section}{\numberline {5.2}Exercises}{596}{section.5.2}%
\contentsline {section}{\numberline {5.3}Construction}{599}{section.5.3}%
\contentsline {section}{\numberline {5.4}Exercises}{635}{section.5.4}%
\contentsline {chapter}{\numberline {A} Vectors}{639}{appendix.A}%
\contentsline {section}{\numberline {A.1}$2\times 1$ vectors}{639}{section.A.1}%
\contentsline {section}{\numberline {A.2}$3\times 1$ vectors}{647}{section.A.2}%
\contentsline {chapter}{\numberline {B}Matrices}{651}{appendix.B}%
\contentsline {section}{\numberline {B.1}Eigenvalues and Eigenvectors}{651}{section.B.1}%
\contentsline {section}{\numberline {B.2}Determinants}{652}{section.B.2}%
\contentsline {section}{\numberline {B.3}Rank of a Matrix}{653}{section.B.3}%
\contentsline {section}{\numberline {B.4}Inverse of a Matrix}{654}{section.B.4}%
\contentsline {section}{\numberline {B.5}Orthogonality}{655}{section.B.5}%
\contentsline {section}{\numberline {B.6}Singular Value Decomposition}{656}{section.B.6}%
\contentsline {chapter}{\numberline {C}Triangle Constructions}{659}{appendix.C}%
\contentsline {chapter}{\numberline {D}Linear Forms}{663}{appendix.D}%
\contentsline {section}{\numberline {D.1}Two Dimensions}{663}{section.D.1}%
\contentsline {section}{\numberline {D.2}Three Dimensions}{669}{section.D.2}%
\contentsline {chapter}{\numberline {E}Quadratic Forms}{681}{appendix.E}%
\contentsline {section}{\numberline {E.1}Conic equation }{681}{section.E.1}%
\contentsline {section}{\numberline {E.2}Circles}{686}{section.E.2}%
\contentsline {section}{\numberline {E.3}Standard Form}{691}{section.E.3}%
\contentsline {chapter}{\numberline {F}Conic Parameters}{697}{appendix.F}%
\contentsline {section}{\numberline {F.1}Standard Form}{697}{section.F.1}%
\contentsline {section}{\numberline {F.2}Quadratic Form }{699}{section.F.2}%
\contentsline {chapter}{\numberline {G}Conic Lines}{701}{appendix.G}%
\contentsline {section}{\numberline {G.1}Pair of Straight Lines}{701}{section.G.1}%
\contentsline {section}{\numberline {G.2}Intersection of Conics}{705}{section.G.2}%
\contentsline {section}{\numberline {G.3} Chords of a Conic}{705}{section.G.3}%
\contentsline {section}{\numberline {G.4} Tangent and Normal}{712}{section.G.4}%