ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD

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 q1 and q2 with +ve x-axis respectively.
Vectors V1 and V2
STEP #01
Resolve vector v1 into two rectangular components v1x and v1y.
Magnitude of these components are:
magnitude of v1x
and
magnitude of v1y
STEP #02
Resolve vector vector v2 into two rectangular components vector v2xand vector v2y.
Magnitude of these components are:
vector v2x
and
vector v2y
STEP #03
Now move vector vector v2 parallel to itself so that its initial point (tail) lies on the terminal point (head) of vector vector v1 as shown in the diagram.
vector v1 and v2
Representative lines of v1 and v2 are OA and OB respectively. Join O and B which is equal to resultant vector of v1and v2
STEP #04
Resultant vector along X-axis can be determined as:
resultant vector
STEP # 05
Resultant vector along Y-axis can be determined as:
resultant vector
STEP # 06
Now we will determine the magnitude of resultant vector.
In the right angled triangle DBOD:
HYP2 = BASE2 + PERP2
magnitude of resultant vector
STEP # 07
Finally, the direction of resultant vector will be determined.
Again in the right angled triangle DBOD:
right angled triangle
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.