IITJEE Advance • Mathematics New Syllabus
Module 14: Vector Algebra Hub
Master the geometry of directed line segments and multi-dimensional spaces. Explore dot and cross products, scalar and vector triple products, and rigorous geometric applications.
Topic 1.1 • Fundamentals
Vectors and Scalars, Addition of Vectors, Collinearity, and Components in 2D/3D
Topic 1.2 • Vector Geometry
Direction Cosines, Direction Ratios, Unit Vectors, and Section Formula
Topic 2.1 • Scalar Product
Scalar (Dot) Product, Angle Between Vectors, Orthogonality, and Projections
Topic 2.2 • Vector Product
Vector (Cross) Product, Properties, Area of Triangles and Parallelograms
Topic 3.1 • Box Product
Scalar Triple Product (STP), Coplanarity of Vectors, and Volume of a Parallelepiped
Topic 3.2 • Advanced Products
Vector Triple Product (VTP) Evaluation, Lagrange’s Formula, and Scalar Tetrads
Topic 4.1 • Advanced Algebra
Solving Linear Vector Equations, Reciprocal System of Vectors, and Basis Vectors
Topic 4.2 • Applications