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The present book aims at providing a detailed account of the basic concepts of vectors that are needed to build a strong foundation for a student pursuing career in mathematics. These concepts include—Addition and Multiplication of vectors by Scalars, Centroid, Vector Equations of a Line and a Plane and their application in Geometry and Mechanics, Scalar and Vector product of two vectors, Differential and Integration of vectors, Differential Operators, Line Integrals, and Gauss’s and Stoke’s Theorems. It is primarily designed for B.Sc and B.A. Courses, elucidating all the fundamental concepts in a manner that leaves no scope for illusion or confusion. The numerous high-graded solved examples provided in the book have been mainly taken from the authoritative textbooks and question papers of various university and competitive examinations which will facilitate easy understanding of the various skills necessary in solving the problems. In addition, these examples will acquaint the readers with the type of questions usually set at the examinations. Furthermore, practice exercises of multiple varieties have also been given, believing that they will help in quick revision and in gaining confidence in the understanding of the subject. Answers to these questions have been verified thoroughly. It is hoped that a thorough study of this book would enable the students of Mathematics to secure high marks in the examinations. Besides students, the teachers of the subject would also find it useful in elucidating concepts to the students by following a number of possible tracks suggested in the book. About the Author Hari Kishan is Senior Reader in Mathematics at Kishori Raman Postgraduate College, Mathura, affiliated to Dr. Bhim Rao Ambedkar University, Agra. He has 34 years of teaching experience of degree classes to his credit. He completed his M.Sc. from B.S.A. College, Mathura in 1971 and obtained a record percentage of marks for which he was awarded Gold Medal by Agra University. He received Ph.D. degree in Mathematics (Fluid Dynamics) in 1981 from the same university. His topic of research was ‘Flow of Homogeneous or Stratified Viscous Fluids.’ He has got published numerous research papers in several mathematical journals of repute. Besides, he is a well-known author of a large number of books on Mathematics, including Trigonometry, Differential Calculus, Integral Calculus, Coordinate Geometry of Two Dimensions, Coordinate Geometry of Three Dimensions, Matrices, Modern Algebra, Theory of Equations, Dynamics, Statics, Hydro Statics, Real Analysis, Numerical Analysis and Sure Success in Convergence. Table of Contents 1. Definitions, Addition of Vectors, Multiplication of Vectors by Scalars 2. Centroid 3. Vector Equations of a Line and a Plane : Application in Geometry and Mechanics 4. Scalar Product of Two Vectors 5. Vector Product of Two Vectors 6. Multiple Products 7. Further Application of Vectors to Geometry and Mechanics 8. Differentiation of Vectors 9. Integration of Vectors 10. Differential Operators 11. Line Integrals, Gauss’s and Stoke’s Theorems