What is vector and what are the basics concepts of vectors

What is vector and what are the basics concepts of vectors:
Firstly i will tell you that what is vector.
Vector:
A vector is represented graphically by a directed line segment with an arrow head. The length of line segment according to the chosen scale correspond to the magnitude of the vector.
Rules applicable on vectors:
Vectors cannot be added subtracted multiplied and divided by simple arithmetic rule. We graphic and trigonometric rules for vectors.
Vectors representations:
There are two ways to represent vectors quantities.
1.      Symbolic representations
2.      Graphical representations.
1. Symbol representation
A vector represented by bold letter A.

OR

A vector may also be represented by putting an arrow above or below the letter as A or A.

The magnitude of a vector is also called modulus and is denoted by placing two parallel lines across a vector, i.e.           A   =A
2.      Graphically representations:
A vector is graphically represented by a straight line arrow head at the end in the direction of the vector. The length of the line according to scale gives the magnitude of the vector.

Rectangular coordinate system:
It has two types
1.     Two dimensional coordinate system:
In plane two straight lines drawn perpendicular to each other are called coordinate axes.

The two lines are called x and y-axis. X-axis taken along horizontal direction and Y-axis taken along vertical direction.
                                         
                                    
                                                                                                   




2.     Three dimensional coordinate system:
It consist of three straight lines perpendicular to each other in space the three lines are called X,Y and Z-axes. As show in fig.

                                 

                                                                                             
Definitions of Vectors types:
Resultant Vector:
The sum of two or more vectors called resultant vector. It ha effect as combined effect of vector which are to be added.
Example:
Consider two vectors A and then their resultant R is
R= A + B


Unit Subtractions:
Add the negative of the vector by head to tail rule the resultant vector will give the subtraction or difference between the two vectors.
Null Vector:
A vector which has one or unit magnitude in a particular direction.
Null vector:
A vector of zero magnitude is called null vector. It is denoted by O the null vector has arbitrary direction. It can be obtained by subtracting two similar vectors. We cannot represent it on the paper.
A-A=O
Equal vector:
Two vectors A and B are said to be equal vector if they have the same magnitude direction.
                                                                                                           A


                                                                                                                             

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