Definition of Vectors

 

Introduction

In life there are objects that can be fully described by only one number. For example, if we want to know how much money we have in our pocket (liquidity), only one number is sufficient to inform us. 

For other type of objects this is not enough. For example, if we want to describe the force that is applied to an object, we have to define the magnitude, as well as the direction of the force that it is applied. The packet containing magnitude and direction is called vector.

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Vectors and Rectangular Coordinates

 

Unit Vectors

Consider the Cartesian coordinate system in space. On each of its dimensions x,y and z, we define respectively the vectors:

These vectors are independent between them and have magnitude (length) of one:

We call these vectors, unit vectors. Every other vector in this space can be constructed by adding multiples of these unit vectors. Or, a vector can be decomposed in components, in multiples of unit vectors, at all dimensions. So the vector in Image 1 can be constructed by adding:

Read more: Vectors and Rectangular Coordinates