Vector Addition

* Vector is the quantity which has magnitude and * Vector is the quantity which has magnitude and directiondirection*Vector is symbolyzed by the shape of an arrow*Vector is symbolyzed by the shape of an arrow

*Vector can be added, subtracted and *Vector can be added, subtracted and multipliedmultiplied

Head / end point

Tail / initial point

A

- A

A

B

C

A + B = C

AD

A + (-B) = D

A – B = D

- B

Vector AdditionVector Addition1.1. PARALLELOGRAM METHODPARALLELOGRAM METHOD

2.2. CC OSINE METHODOSINE METHOD

3.3. POLYGON METHODPOLYGON METHOD

4.4. ANALYTIC METHODANALYTIC METHOD

PARALLELOGRAM METHODPARALLELOGRAM METHOD

1. Make the 1. Make the parallelogram shape parallelogram shape by draw the vectors by draw the vectors again in same size again in same size and directionand direction

A

B



A

B



A

B



2.The vector sum is 2.The vector sum is the line that connect the line that connect the central point to the central point to the its front cornerthe its front corner

A

B

R

COSINE METHODCOSINE METHOD

1. The vector sum is 1. The vector sum is

R= R= √ A√ A22 + B + B22 + 2AB cos + 2AB cos αα

A

B

αα

COSINE METHODCOSINE METHOD

1. The vector sum is 1. The vector sum is

R= R= √ A√ A22 + B + B22 + 2AB cos + 2AB cos αα

2. The direction is 2. The direction is

Sin Sin ββ = A . Sin = A . Sin αα / R / R

A

B

αα ββ

R

POLYGON METHODPOLYGON METHOD(for more than 2 vectors)(for more than 2 vectors)

1.Connect all the 1.Connect all the vectors orderly from vectors orderly from initialpoint to endpoint initialpoint to endpoint of each vectorof each vector A

B

C

POLYGON METHODPOLYGON METHOD(for more than 2 vector)(for more than 2 vector)


BC



B

C


1.Connect all the 1.Connect all the vectors orderly from vectors orderly from initialpoint to endpoint initialpoint to endpoint of each vectorof each vector

2. The resultant is the 2. The resultant is the line that connecting line that connecting from initialpoint to from initialpoint to endpointendpoint

A

B

C

R

ANALYTIC METHODANALYTIC METHOD

1.Connect all the 1.Connect all the initialpoint of the initialpoint of the vectorsvectors

A

B

C


1.Connect all the 1.Connect all the initialpoint of the initialpoint of the vectors at cartesian’s vectors at cartesian’s coordinatecoordinate A

B

C


1.Connect all the 1.Connect all the initialpoint of the initialpoint of the vectors at cartesian’s vectors at cartesian’s coordinatecoordinate

A

B

C



A

B

C



A

B

C



2. Find the component 2. Find the component along the x and y axisalong the x and y axis

A

B

C




A

B

C




A

B

C




A

B

C




A

B

C




A

B

C




A

B

C




(you can neglect the (you can neglect the vector)vector)

A

B

C




(you can neglect the (you can neglect the vector)vector)


3. Use the table to find 3. Use the table to find the resultant of each the resultant of each axisaxis

X-AXISX-AXIS Y-AXISY-AXIS

AA AXAX AYAY

BB BXBX -BY-BY

CC -CX-CX CYCY

RR RRXX RRYY

A

B

C


X-AXISX-AXIS Y-AXISY-AXIS

AA AAXX AAYY

BB BBXX -B-BYY

CC -C-CXX CCYY

RR RRXX RRYY

4. Based on R4. Based on RX X andand RRYY calculate the vector sum calculate the vector sum

using formula: R = using formula: R = √ √ RRX X 22

++ RRYY22

the resultant’s direction is: Tg the resultant’s direction is: Tg αα = = RRY Y / R/ RXX

PRACTICEPRACTICE

Find the vector resultant of these vectors Find the vector resultant of these vectors using polygon and analytic methods. using polygon and analytic methods. F1+F2+F3 = …F1+F2+F3 = …

300

F1

600

F2

300

F3

Polygon methodPolygon method

600

F2

300

F3300

F1


300

F3300

F1600

F2


300

F1600

F2

300

F3


300

F1600

F2

300

F3

Analytic methodAnalytic method

300

600300

F1

F2

F3

Documents

Vector Addition