3.5 — The scalar (dot) product
There are two ways to multiply vectors — both physically useful. The scalar (dot) product returns a number — a scalar. Used whenever “amount of…
3.6 — The vector (cross) product
The second kind of vector product — and the more surprising one. Unlike the dot product (which yields a scalar), the cross product yields a vector —…
3.7 — Worked problems — Chapter 3 toolkit in action
Seven worked problems exercising every Chapter 3 tool. Each has a step-by-step solution tagged with the relevant §3.x section.
3.8 — Practice problems — 20 exercises for mastery
Twenty problems without step-by-step solutions, in three difficulty levels. Final answers at the end.
3.9 — Further reading and references
Chapter 3 built the vector language. To go deeper:
3.10 — Q&A — Frequently asked questions for Chapter 3
Short answers to common vector questions.
Chapter 4 — Motion in 2D and 3D
Projectile, uniform circular, and relative motion in 2D and 3D — position, velocity and acceleration vectors with real-world applications.
4.1 — Position and displacement vectors
In 1D, position was a single number x. In 2D or 3D, we need a position vector that runs from the origin to where the object is.
4.2 — Velocity and acceleration vectors
The time-derivative of vec r(t) is the velocity vector. Second derivative is the acceleration vector. All Chapter 2 kinematic equations become…
4.3 — Projectile motion
A projectile is any object moving only under gravity (no air drag). Examples: soccer ball, arrow, water fountain, artillery shell. The classic…