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Introduction

This chapter introduces the language of vectors in Euclidean space, especially in $\R^3\text{.}$ Vectors let us describe points, displacement, direction, length, angle, area, and volume in a unified way.

We begin with the algebra of vectors and the dot product, then study the wedge product and its three-dimensional incarnation, the cross product. We end with parameterizations of curves and surfaces, which provide the flexible geometric descriptions needed later in the book for differentiation and integration.

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