Have you ever played a treasure hunting game? Most of the time, people looking for these supposedly “treasures” use a map.

1. General Physics 1/2
Science, Technology, Engineering, and Mathematics
General Physics 1
Science, Technology, Engineering, and Mathematics
Lesson 2.2
Vector Addition
Through Analytic
Method

2. 2
Have you ever played a treasure hunting game?
Most of the time, people looking for these
supposedly “treasures” use a map.

3. 3
In literature and film,
a common treasure
map is tattered and
has a signature “x” in
the middle to identify
the location of the
treasure.

4. 4
Each individual path
can be combined and
added to specifically
identify how far and in
what direction you
should go to reach it.

5. 5
How are two or more vectors
added?

6. Learning Competency
At the end of the lesson, you should be able to do the
following:
6
Perform addition of vectors
(STEM_GP12V-Ia-9).

7. Learning Objectives
At the end of the lesson, you should be able to do the
following:
7
● Explain the rules of vector addition and
subtraction.
● Use the graphical method to add vectors.

8. 8
Can you help
the monkey
get its
banana?
Recall of Vectors

9. 9
In what directions
did you go into?
Recall of Vectors

10. 10
What is the total
distance you have
travelled in
bringing the
banana to the
monkey?
Recall of Vectors

11. 11
What is the total
displacement you
have travelled in
bringing the
banana to the
monkey?
Recall of Vectors

12. 12
Two vectors are considered
equal if their magnitudes and
direction are the same.
If two or more vectors are
pointing in the same
direction, it means that they
are parallel to each other.
Vectors in One Dimension

13. 13
When two vectors have
opposite directions but have
the same magnitude, they
are called antiparallel.
Vectors in One Dimension

14. 14
What is the difference between
parallel and antiparallel
vectors?

15. 15
What are the rules in adding
and subtracting vectors?

16. 16
Suppose a person has a displacement of A eastward.
Addition of Vectors

17. 17
Suppose he covered an additional displacement B eastward.
Addition of Vectors

18. 18
The initial point of the total displacement is the starting
point of A while the endpoint is the endpoint of B.
Addition of Vectors

19. 19
The total displacement is called the resultant, R.
Addition of Vectors

20. 20
The addition (and subtraction) of vectors can be done using
the head to tail method.
Addition of Vectors
tail head head
tail

21. 21
Suppose a person has a displacement of A eastward.
Subtraction of Vectors

22. 22
Suppose he covers another displacement of B westward.
Subtraction of Vectors

23. 23
The resultant R can be measured using head to tail method.
Subtraction of Vectors

24. 24
The resultant R can be measured using head to tail method.
Subtraction of Vectors

25. 25
● Most of the vectors that you will encounter are not
always parallel or antiparallel.
● However, the same rules for the addition of vectors
apply even if there are specific angles given.
● Head to tail method can still be used in adding vectors
while considering their angles.
Graphical Method of Adding Vectors

26. 26
We can add vectors by placing them head to tail.
Graphical Method of Adding Vectors

27. 27
Adding them in reverse gives the same result. This is the
commutative law of addition.
Graphical Method of Adding Vectors

28. Remember
28
When you add two or more vectors,
they should contain similar units and
should describe the same physical
quantity. For example, a displacement
vector can only be added to another
displacement vector. It does not make
sense to add it to a velocity vector, for
example.

29. 29
How are vectors added
graphically?

30. 30
● Vectors can be added graphically (geometrically) or
algebraically.
● A graphing paper or a bond paper, a ruler, and a
protractor are needed in adding vectors graphically.
Graphical Method of Adding Vectors

31. Let’s Practice!
31
A car initially traveled 35 km due south and then
traveled 65 km to the west. What is the car’s
resultant displacement?

32. Let’s Practice!
32
A car initially traveled 35 km due south and then
traveled 65 km to the west. What is the car’s
resultant displacement?
The resultant displacement is 74 km, 28°.

33. Try It!
33
33
What is the resultant displacement if a
man jogs 120 m, east and then walks 50
m due south?

34. Try It!
34
34
Philip jogged along the street and
covered 110 m north. He stopped for
a while and jogged for another 20 m
north. What is his total
displacement?

35. Try It!
35
35
A student walks 10 m east and 6 m
north. What is her resultant
displacement?

36. Remember
36
The vector sum or resultant may vary
from one individual to another due to
the limitations of our measuring
devices such as the ruler and the
protractor. However, this deviation
should only be by a few millimeters and
a few degrees.

37. Let’s Sum It Up!
37
● The sum of the vectors is called the resultant, R.
● Vectors are considered equal only if they have the
same magnitude and direction.
● Parallel vectors are those that are pointing in
the same direction. On the other hand,
antiparallel vectors are those that are in

38. Let’s Sum It Up!
38
● Vector addition follows the commutative and
associative laws of addition.
● Vectors can be added graphically using the head
to tail method.

39. Bibliography
39
Bauer, W., and Gary D. Westfall. University Physics with Modern Physics. New York: McGraw-Hill,
2013.
Faughn, Jerry S. and Raymond A. Serway. Serway’s College Physics (7th ed). Singapore: Brooks/Cole,
2006.
Knight, Randall Dewey. Physics for Scientists and Engineers: a Strategic Approach with Modern
Physics. Pearson, 2017.
Serway, Raymond A. and John W. Jewett, Jr. Physics for Scientists and Engineers with Modern Physics (9th
ed). USA: Brooks/Cole, 2014.
Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky’s University Physics with
Modern Physics (13th ed). USA: Pearson Education, 2012.