To do

Work out some concrete problems, especially checking for angles, lengths, perpendicularity.

Given vectors work out a formula for for which is perpendicular to . The resulting vector is said to be the projection of on . See why it is so, by examining some plane examples. In general, it makes a similar sense in higher dimensions as well. In general, the dot product does behave like a commutative multiplication with nice distributive properties over addition:
This means identities like ( ). .
The main thing which does not make sense is a dot product of three vectors, since the product of two produces a scalar and not a vector!

Special attention should be given to problesm 18-24 on pages 18,19.

Also do the problems from the WQS system based on Chapter 1.2.