Chapter 3 built the vector language. To go deeper:
Books
In physics
- Halliday, Resnick, Krane — Physics Vol 1, Ch 3. Primary reference
- Griffiths — Introduction to Electrodynamics, Ch 1. The first chapter is a full vector course, excellent for physics students
In mathematics
- Marsden & Tromba — Vector Calculus. Classic for engineering and physics
- Boas — Mathematical Methods in the Physical Sciences, Ch 3. Physicist's angle on vectors
For deeper intuition
- Feynman Lectures Vol I, Ch 11 — "Vectors", outstanding. Ch 20 on rotational vectors too.
Free online resources
Video series
- 3Blue1Brown — Essence of Linear Algebra. Unrivaled animations for vector intuition. 3 hours
- MIT OCW 18.02 (Multivariable Calculus) — vector and product lectures
- Khan Academy — Vectors — Vectors lessons
Simulations
- PhET Vector Addition — Adding vectors
- GeoGebra 3D — 3D vector plotting interactively
Immediate uses in later chapters
- Ch 4 — 2D motion: projectile as
\vec r = x\hat i + y\hat j - Ch 5-6 — Newton's laws:
\vec F = m\vec a, all vector - Ch 8 — work and energy:
W = \int \vec F \cdot d\vec r(dot product + integral) - Ch 10-11 — torque and angular momentum:
\vec \tau = \vec r \times \vec F - Ch 29 — electric/magnetic fields: vectors in space
- Ch 32 — Maxwell's equations:
\nabla \cdot \vec E,\nabla \times \vec B(vector calculus, Ch 15 in Griffiths)
Real-world uses of vectors
- Computer graphics — every pixel, every rotation, every animation is vectors
- Video games — vector physics for collisions, throws, motion
- Navigation — GPS uses vectors on the Earth's surface
- Robotics — robot arm, vectors in joint space
- AI — words as vectors in embedding space
- Quantum mechanics — states as vectors in Hilbert space
Topics this chapter didn't cover
- Vector calculus:
\nabla f(gradient),\nabla \cdot \vec F(divergence),\nabla \times \vec F(curl). Essential in electromagnetism and fluid dynamics. - Vectors in non-Euclidean spaces: for special and general relativity
- Tensors: the generalization to "multi-directional". Stress tensor, moment of inertia tensor
Preview of §3.10
Frequently asked questions about vectors — the questions students commonly raise.
📚 A great book for all physics: Div, Grad, Curl and All That by H.M. Schey — a short intuitive intro to vector calculus.
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