Vector Addition

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

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

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

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

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)

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

BC

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

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)

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

ANALYTIC METHODANALYTIC METHOD

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

ANALYTIC METHODANALYTIC METHOD

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

ANALYTIC METHODANALYTIC METHOD

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

ANALYTIC METHODANALYTIC METHOD

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

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

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

A

B

C

ANALYTIC METHODANALYTIC METHOD

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

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

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

ANALYTIC METHODANALYTIC METHOD

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

ANALYTIC METHODANALYTIC METHOD

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 methodsusing polygon and analytic methods

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