The document describes several methods for finding the vector sum (resultant) of two or more vectors, including: 1. The parallelogram method draws the vectors to form a parallelogram, with the resultant being the diagonal. 2. The cosine method uses a formula involving the magnitudes of the vectors and the angle between them. 3. The polygon method connects the vectors tip to tail to form a polygon, with the resultant connecting the initial and final points. 4. The analytic method resolves the vectors into their x and y components, sums the respective components, and determines the resultant's magnitude and direction from the sums and a formula.

1. Vector Addition PARALLELOGRAM METHOD C OSINE METHOD POLYGON METHOD ANALYTIC METHOD

2. PARALLELOGRAM METHOD 1. Make the parallelogram shape by draw the vectors again in same size and direction A B

3. PARALLELOGRAM METHOD 1. Make the parallelogram shape by draw the vectors again in same size and direction A B

4. PARALLELOGRAM METHOD 1. Make the parallelogram shape by draw the vectors again in same size and direction A B

5. PARALLELOGRAM METHOD 1. Make the parallelogram shape by draw the vectors again in same size and direction 2.The vector sum is the line that connect the central point to the its front corner A B R

6. COSINE METHOD 1. The vector sum is R= √ A 2 + B 2 + 2AB cos α A B α

7. COSINE METHOD 1. The vector sum is R= √ A 2 + B 2 + 2AB cos α 2. The direction is Sin β = A . Sin α / R A B α β R

8. POLYGON METHOD (for more than 2 vectors) 1.Connect all the vectors orderly from initialpoint to endpoint of each vector A B C

9. POLYGON METHOD (for more than 2 vector) 1.Connect all the vectors orderly from initialpoint to endpoint of each vector A B C

10. POLYGON METHOD (for more than 2 vector) 1.Connect all the vectors orderly from initialpoint to endpoint of each vector A B C

11. POLYGON METHOD (for more than 2 vector) 1.Connect all the vectors orderly from initialpoint to endpoint of each vector 2. The resultant is the line that connecting from initialpoint to endpoint A B C R

12. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors A B C

13. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate A B C

14. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate A B C

15. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate A B C

16. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate A B C

17. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

18. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

19. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

20. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

21. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

22. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

23. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis A B C

24. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis (you can neglect the vector) A B C

25. ANALYTIC METHOD 1.Connect all the initialpoint of the vectors at cartesian’s coordinate 2. Find the component along the x and y axis (you can neglect the vector)

26. ANALYTIC METHOD 3. Use the table to find the resultant of each axis A B C CY -CX C R Y R X R -BY BX B AY AX A Y-AXIS X-AXIS

27. ANALYTIC METHOD 4. Based on R X and R Y calculate the vector sum using formula: R = √ R X 2 + R Y 2 the resultant’s direction is: Tg α = R Y / R X C Y -C X C R Y R X R -B Y B X B A Y A X A Y-AXIS X-AXIS

28. PRACTICE Find the vector resultant of these vectors using polygon and analytic methods 30 0 60 0 30 0