IITJEE Mains • Mathematics New Syllabus
Module 12: Vector Algebra Hub
Master the geometry of directed line segments. Explore vector addition, dot and cross products, scalar triple products, and their geometrical and physical applications.
Topic 1.1 • Fundamentals
Scalars and Vectors, Types of Vectors, Position Vector, and Direction Cosines/Ratios
Topic 1.2 • Vector Addition
Addition of Vectors, Triangle and Parallelogram Laws, and Multiplication by a Scalar
Topic 2.1 • Components
Components of a Vector in 2D and 3D space, and Internal/External Section Formula
Topic 2.2 • Scalar Product
Scalar (Dot) Product, Angle between Two Vectors, and Projections on a Line
Topic 3.1 • Vector Product
Vector (Cross) Product, Right-Hand Rule, and Area of Parallelogram/Triangle
Topic 3.2 • Box Product
Scalar Triple Product, Coplanarity of Three Vectors, and Volume of Parallelepiped
Topic 4.1 • Vector Triple Product
Vector Triple Product (VTP) Evaluation and Lagrange’s Expansion Formula
Topic 4.2 • Applications