The following are my lecture notes on the basics of vectors.

I've broken these into 3 lectures. The first lecture deals with the basic geometry and the coordinatization of vectors to include scalar multiplication, addition, and subtraction of vectors. This includes a discussion of the i-j form of a vector.

To see animated examples of the addition of vectors see the velocity vector applications on the trigonometry applications page.

The second lecture deals exclusively with the dot product and  the third deals with the cross product.