## Physics XI Content

# ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD

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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 q and _{1}q with +ve x-axis respectively._{2} | |||

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: | |||

HYP ^{2} = BASE^{2} + PERP^{2 } | |||

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. |