← IB Class AA
Vectors
Chapter Overview
Vector representation, magnitude, unit vectors. Addition, scalar multiplication. Dot product for angle between vectors and projection. Vector equation of a line. For HL: cross product, vector and Cartesian equations of planes, intersection of lines and planes, distances.
Topics Covered
- Vector Basics
- Dot Product
- Angle Between Vectors
- Vector Equation of Line
- Cross Product (HL)
- Plane Equations (HL)
- Intersections (HL)
- Shortest Distance (HL)
Key Formulas
A.B = |A||B|cos A
A.B = a1b1 + a2b2 + a3b3
r = a + tb (line)
|A x B| = |A||B| sin A (HL)
Real-World Applications
Applications: Physics (mechanics), 3D graphics, robotics, navigation systems.
Study Tips
Tip: Visualize vectors geometrically
Tip: Master dot product applications
Tip: Practice 3D visualization for HL