### 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