ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD



ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD
INTRODUCTION
Rectangular component method of addition of vectors is the most simplest method to add a number of vectors acting in different directions.
DETAILS OF METHOD
Consider two vectors  making angles q1 and q2 with +ve x-axis 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
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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 X-axis can be determined as:
STEP # 05
Resultant vector along Y-axis can be determined as:
STEP # 06
Now we will determine the magnitude of resultant vector.
In the right angled triangle DBOD:
HYP2 = BASE2 + PERP2
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 X-axis.
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.