This is the beginning of an online course to get to grips with 3D vectors for anyone who wants to learn. Most of the material is about UK A-level difficulty, so if you're studying a maths course involving vectors I hope working through it won't harm your grades:) Also if you're interested in related topics, such as 3D graphics programming or Newtonian mechanics, I hope you'll find something useful or interesting.

Good luck with the course!...

- 3D Vectors
- The Dot Product
- The Cross Product
- The Vector Equation of a Line
- The Vector Equation of a Plane
- The Point of Intersection of a Line and a Plane
- Some Shortest Distance Calculations
- Coordinate Systems
- An introduction to parametric curves

Testing what you know...

- Challenge 1: The distance between two cities along the surface of the Earth
- Challenge 2: Docking at a space station
- Tim's Challenge: The angle between two adjacent sides of a dodecahedron
- Using vectors: a simple molecular modeller

- Great circle applet
- Molecular modeller applet
- Dot product applet
- Cross product applet
- Dodecahedron applet
- Distance to a plane applet
- Parametric curves applet
- Parametric surfaces applet

Apologies for the extremely slow progress - finals seem to be taking up most of my time at the moment. Many thanks for the encouragement though, and I hope I can get round to improving the site before long.

- An applet to help explain parametric vector equations - curves in 3D space.
- Trajectories - Keplers' laws of planetary motion and conic sections.
- Linear transformations between vector spaces, rotations, reflections, scalings...
- The intersection of 3 planes
- Volume of a parallelepiped (used in crystallography and xray diffraction)
- Eigenvalues and eigenvectors
- Complex numbers (isomorphic to 2D vectors)

If you found the above simple and are curious about what a vector really is here's a page introducing the concept of a vector space.

Please e-mail me (Paul Kirby) if you have any suggestions, improvements, find any errors, think some part is unclear, or just want to:)

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