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.