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