### Introduction

There are two kinds of multiplication involving vectors. The first is known as the
**
scalar product
**
or
**
dot product
**
. This is so-called because when the scalar product of two vectors is calculated the result is a scalar. The second product is known as the
**
vector product
**
. When this is calculated the result is a vector. The definitions of these products may seem rather strange at first, but they are widely used in applications. In this Section we consider only the scalar product.

#### Prerequisites

- know that a vector can be represented as a directed line segment
- know how to express a vector in Cartesian form
- know how to find the modulus of a vector

#### Learning Outcomes

- calculate, from its definition, the scalar product of two given vectors
- calculate the scalar product of two vectors given in Cartesian form
- use the scalar product to find the angle between two vectors
- use the scalar product to test whether two vectors are perpendicular

#### Contents

1 Definition of the scalar product2 A formula for finding the scalar product

3 Resolving one vector along another

4 Using the scalar product to find the angle between vectors

5 Vectors and electrostatics

6 Engineering Example 1

6.1 Field due to point charges