Class 12 NCERT • Mathematics Part 2 (New Syllabus)
Mathematics Part 2 Ch 10: Vector Algebra
Select a topic or study module below to explore basic vector concepts, types of vectors, addition, scalar multiplication, components, direction cosines and ratios, scalar (dot) product, vector (cross) product, projection of vectors, and comprehensive textbook problem solutions.
Topic 01 • Vector Basics & Types
Exploring Directed Line Segments, Magnitude, Direction, Zero, Unit, Co-initial, Collinear, and Equal Vectors
Topic 02 • Addition & Scalar Multiplication
Analyzing Triangle Law, Parallelogram Law of Vector Addition, Properties, and Scalar Multiple Scaling Laws
Topic 03 • Components & Position Vectors
Studying Three-Dimensional Cartesian Coordinates, Position Vector r = xi + yj + zk, and Magnitude Formulas
Topic 04 • Direction Cosines & Ratios
Investigating Angles with Coordinate Axes (l, m, n), Identity l2 + m2 + n2 = 1, and Direction Ratios
Topic 05 • Scalar (Dot) Product
Examining Geometric Meaning, Angle Between Two Vectors, Orthogonality Condition (a • b = 0), and Component Multiplications
Topic 06 • Projection of Vectors
Analyzing Scalar and Vector Projections, Formula derivations using Dot Products, and Geometric Applications
Topic 07 • Vector (Cross) Product
Studying Right-Handed System, Determinant Expansion for Cross Products, Area of Triangles and Parallelograms
Module 08 • Solutions & Chapter Review