Addition of vectors by rectangular components method
1. 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 and 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.
2. 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 BOD:
3. HYP2 = BASE2 + PERP2
STEP # 07
Finally the direction of resultant vector will be determined.
Again in the right angled triangle BOD:
Where 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.
