Unit Vectors and Vectors in Space

                                Unit Vectors and Vectors in Space

    A vector is called a unit vector if it has magnitude = 1
, then the unit vector in the  If a vector
direction of v can be found by :
                     
 
 Example:
 is   the unit vector in the direction of     
 
 
Since:

Example:
 find the unit vector in the direction of v .  Let    
 Solution :
              
   

Vectors in space:

Addition, Subtraction and Scalar Multiplication for vectors in space:
,and and     For any vectors  for any scalar c,
              
             
             

The Vector between Two points:

is: to       The vector from
                       
 Example:
is: to       The vector from
                       

Length and Direction:
 
 is    The length of the vector
 

Example:
 find the length of A.     Let

Solution:
 
 
      
Example:
      Find a unit vector u in the direction of the vector from
 

Solution:
     

Distance in Space:
     The distance between
                  

Example:
  is: The distance between       
                             
 Exercise:               
      (1) Find a unit vector u in the direction of the vector from
 
.            (2) Find the distance between