Physics XI Content
ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD


INTRODUCTION


Rectangular component method of addition of vectors is the simplest method to add a number of vectors acting in different directions.  
DETAILS OF METHOD


Consider two vectors making angles q_{1} and q_{2} with +ve xaxis respectively.  
STEP #01


Resolve vector into two rectangular components and .  
Magnitude of these components are:  
and 

STEP #02


Resolve vector into two rectangular components and .  
Magnitude of these components are:  
and 

STEP #03


Now move vector parallel to itself so that its initial point (tail) lies on the terminal point (head) of vector as shown in the diagram.  
Representative lines of and are OA and OB respectively. Join O and B which is equal to resultant vector of and  
STEP #04


Resultant vector along Xaxis can be determined as:  
STEP # 05


Resultant vector along Yaxis can be determined as:  
STEP # 06


Now we will determine the magnitude of resultant vector.  
In the right angled triangle DBOD:  
HYP^{2} = BASE^{2} + PERP^{2
}


STEP # 07


Finally, the direction of resultant vector will be determined.  
Again in the right angled triangle DBOD:  
Where q is the angle that the resultant vector makes with the positive Xaxis. In this way we can add a number of vectors in a very easy manner. This method is known as ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD. 