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Quaternions came from Hamilton \(\ldots\) and have been an unmixed evil to those who have touched them in any way. Vector is a useless survival \(\ldots\) and has never been of the slightest use to any creature.
–Lord Kelvin
In this chapter we consider the basic operations on vectors in two- and three-dimensional space: vector addition, scalar multiplication, and the dot and cross products. In Section 11.7 we generalize some of these notions to \(n\)-space and discuss properties of matrices that will be needed in later Chapters.