ADDITION OF VECTORS-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.

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