Vectors in the Plane

                                                Vectors in the Plane:

Notation:
       A directed line segment is defined as an initial point
and a terminal point Q .

       Example:
   P = (2,3) and Q = (-1,4) .

       Example:
    The four vectors having the same length and direction . They therefore represent the same vector, and we write :
The vector AB = vector CD = vector OP = vector EF .
Notation:
   The vector defined by the directed line segment from point A  to point B and written as (vector AB) means
Components :
   the vector  Whenever a vector v can be written as
   are said to be components of v . 
Notation:
are the vector components of   and  , the vector   If  .The numbers a and b are the  and  in the directions of 
 . and  in the directions of   scalar components of 

Algebraic Addition :
 ,then and     If
 .             
       Example:
 

  Subtraction:
,then and     If
 .             

       Example:
 
Exercise:
 find: and     (1)If
  (a)
  (b)
find: and     (2) If
  (a)
  (b)

Properties of Vector Addition and Subtraction:
                     
    We have the following four properties of vectors:
If u, v and w are vectors and a and b are numbers then:
(1) ( u + v) + w = u + (v + w)
(2) a ( u + v)  = au + av
(3) a ( bv)  = (ab) v
(4) u + v = v +u.