← GSEB Class 12
Vector Algebra
Chapter Overview
Vectors have magnitude and direction, represented as directed line segments. Types: zero, unit, position, equal, collinear, coplanar. Operations: addition (triangle/parallelogram law), scalar multiplication, dot product (scalar result, A.B = |A||B|cos A), cross product (vector result, |A x B| = |A||B| sin A, direction right-hand rule). Section formula for vectors.
Topics Covered
- Vector Types and Notation
- Position Vectors
- Addition of Vectors
- Multiplication by Scalar
- Dot Product
- Cross Product
- Scalar Triple Product
- Vector Triple Product
- Section Formula
Key Formulas
A.B = |A||B|cos A
A x B = |A||B|sin A n^
|A x B| = area of parallelogram
A.B = 0 if perpendicular
A x B = 0 if parallel
Real-World Applications
Applications: Physics (force, velocity, torque), computer graphics, navigation, engineering mechanics.
Study Tips
Tip: Understand the geometric meaning of dot and cross products
Tip: Practice vector addition with diagrams
Tip: Learn right-hand rule for cross products