Vectors: dot and cross products

Lengths, the dot product, the angle between vectors and the cross product, by hand. About 9 minutes, A-level.

What you will do

1. A vector is a move. A vector gives how far to go along each axis. Its length comes from Pythagoras.
2. The dot product. Multiply matching components and add. The answer is a number, and it is 0 when the vectors are perpendicular.
3. Perpendicular vectors. A dot product of 0 means a 90° angle.
4. The cross product. In 3D the cross product is a vector perpendicular to both, and its length is the area of the parallelogram they span.