Watch

Two Recorded Lectures

Each video runs at least eight minutes, with every example worked on screen rather than read from a slide. Watch the first after Lesson 03 and the second after Lesson 05 — they are summaries, not substitutes for reading the lessons.

≈ 9 min · covers Lessons 01–03

Video Lesson I

Lines and Planes: Every Form, and How to Move Between Them

Vector, parametric, symmetric and Cartesian forms; why R² and R³ differ; and sketching a plane from its intercepts, all worked on screen.

What it covers

  • Building a line from a point and a direction, and from two points.
  • Converting between all four forms, including the zero-component case.
  • Why one equation gives a line in R² and a plane in R³.
  • The cross product as the bridge between two directions and a normal.
  • Sketching a plane from its three intercepts.

≈ 10 min · covers Lessons 04–05

Video Lesson II

Intersections, Systems and Distances

The three line-and-plane cases worked live, the line of intersection of two planes, and every distance formula applied to a real problem.

What it covers

  • Classifying two lines, including the skew case that only exists in R³.
  • Substituting a line into a plane, and the three ways the algebra can collapse.
  • Finding a line of intersection, and checking it against n₁ × n₂.
  • Every distance formula, and why each one is a projection.
  • The glass-panel problem: the distance between two parallel planes.

A note on the recordings

Nothing is embedded until you click. The page ships a poster image and swaps in the player on the first press, so no third-party script or cookie loads for a visitor who only came to read. Once a recording exists, paste its eleven-character YouTube id into public/assets/js/config.js and both this page and the printed version pick it up.