Differentiate scalar product from vector product.

General Physics
Differentiate scalar product from vector product.

1. General Physics 1/2
Science, Technology, Engineering, and Mathematics
General Physics 1
Science, Technology, Engineering, and Mathematics
Lesson 2.5

Vector Multiplication

2. 2
How does vector multiplication
work? What are the basic rules you
need to keep in mind when
multiplying vectors?

3. Learning Competencies


This lesson serves as an enrichment for the following DepEd competency:


3
Perform addition of vectors (STEM_GP12V-Ia-9).

4. Learning Objectives


At the end of the lesson, you should be able to do the following:


4
●Differentiate scalar product from vector product.

●Identify the applications of scalar product and vector
product.

●Use the right-hand rule to determine the direction of a
vector product.

5. 5
Several physics quantities are defined using products of two other
quantities.
Vector Multiplication
work
torque

6. 6
How does a scalar product differ
from a vector product?

7. 7
Scalar Product
●The scalar product of a vector and another vector will result in a
scalar quantity.

●It is also referred to as a dot product.
Vector Multiplication

8. 8
Scalar Product



●When can the scalar product be positive?

●When can the scalar product be negative?

●When can the scalar product be zero?
Vector Multiplication

9. 9
Scalar Product



●What happens when vectors are parallel?
Vector Multiplication

10. 10
Scalar Product



●What happens when vectors are antiparallel?
Vector Multiplication

11. 11
Scalar Product
Scalar product follows these laws.
Vector Multiplication
Commutative Law
Distributive Law

12. Let’s Practice!


12
Find the scalar product between the two vectors if the
magnitude of A is 9.0 and B is 15.0 and the angle between
them is 45º.

13. Let’s Practice!


13
Find the scalar product between the two vectors it the
magnitude of A is 9.0 and B is 15.0 and the angle between
them is 45º.

The scalar product is 95.

14. Try It!
1414
Find the scalar product between the two
vectors if A has a magnitude of 5 km and B has
a magnitude of 6 km. The angle between them
is 150º.

15. Let’s Practice!


15
Find the magnitude of vector A if the scalar product between
A and B is 30 m, the magnitude of B is 10 m, and the angle
between the vectors is 60º.

16. Let’s Practice!


16
Find the magnitude of vector A if the scalar product between
A and B is 30 m, the magnitude of B is 10 m, and the angle
between the vectors is 60º.


The magnitude of A is 6 m.

17. 17
Vector Product
The vector product or the cross product of two vectors will result in a
vector quantity.
Vector Multiplication

18. 18
Vector Product

Vector Multiplication

19. 19
Scalar Product



●What happens when vectors are parallel?

●What happens when vectors are antiparallel?
Vector Multiplication

20. Remember


20
Do not interchange the expression ABcosɸ and
ABsinɸ. The former is used to calculate the
scalar product of two vectors while the latter is
used to determine the magnitude of the vector
product.

21. 21
Right-Hand Rule
The direction of the vector product lies perpendicular to the plane
containing both vectors.

That direction is determined by the right-hand rule.
Vector Multiplication

22. 22
Right-Hand Rule
Begin by placing two vectors tail to tail.
Vector Multiplication

23. 23
Right-Hand Rule


Point the fingers in your right hand
along A, while your palms face
vector B. Curl your fingers toward
B.
Vector Multiplication

24. 24
Right-Hand Rule
What if you want to determine the
cross product B x A? Will the
results be the same?
Vector Multiplication

25. 25
Right-Hand Rule
Another version of the right-hand
rule uses the index finger, the
middle finger, and the thumb.
Vector Multiplication

26. 26
Vector Product
The following properties apply to vector product.
Vector Multiplication
Anticommutative Property
Distributive Law

27. Let’s Practice!


27
Find the magnitude of the vector product , if is 9 m
along the x-axis and is 12 m located along the xy-plane,
making a 50°-angle with respect to the x-axis.

28. Let’s Practice!


28
Find the magnitude of the vector product , if is 9 m
along the x-axis and is 12 m located along the xy-plane,
making a 50°-angle with respect to the x-axis.
The magnitude of the vector product is 82.73 m.

29. Try It!
2929
What is the magnitude of the cross product of
vectors C and D, if vector C is 5 units along the
y-axis while vector D is 3 units located along
the xy-plane? Vector D makes a 20°-angle with
respect to the y-axis.

30. Let’s Practice!


30
Find the magnitude of vector if the magnitude of the vector
product is 150 m and the magnitude of is 80 m.
The angle between the two vectors is 45°.

31. Let’s Practice!


31
Find the magnitude of vector if the magnitude of the vector
product is 150 m and the magnitude of is 80 m.
The angle between the two vectors is 45°.
The magnitude of vector is 2.65 m.

32. Try It!
3232
Find the magnitude of vector if the
magnitude of the vector product is 50
units and the magnitude of is 20 units. The
angle between the two vectors is 100°.

33. 33

What are examples of scalar and
vector products?

34. Check Your Understanding


34
Identify the word(s) being described in each statement.
1.It is the other name given for a scalar product.
2.It is the other name given for a vector product.
3.It is a property of the scalar product which specifies that even if
the vectors are reversed or moved around, the product would still
be the same.

35. Check Your Understanding


35
Write true if the statement is correct. Otherwise, write false.
1.The scalar product of two vectors is a scalar quantity.
2.The vector product of two vectors is a vector quantity.
3.The magnitude of a vector product can have a negative value.

36. Let’s Sum It Up!


36
●The scalar product of two vectors is a scalar quantity.
○It is also known as a dot product.
○The scalar product between two vectors can be
calculated by multiplying their magnitudes with the
cosine of the angle between them.
○Examples of scalar products are work and electric
potential.

37. Let’s Sum It Up!


37

●The vector product of two vectors results in a vector
quantity.
○It is also known as a cross product.
○The magnitude of the vector product can be calculated
by multiplying the magnitudes of the two vectors with
the sine of the angle between them.

38. Let’s Sum It Up!


38

●The vector product of two vectors results in a vector
quantity.
○The direction of the vector product can be determined
using the right-hand rule.
○Examples of vector products are torque and angular
momentum.

39. Let’s Sum It Up!


39






●Both kinds of multiplication have the distributive
property. However, only the scalar product has a
commutative property. The vector product, on the other
hand, has an anticommutative property.

40. Key Formulas


40
Concept Formula Description
Scalar or Dot Product

where
●A is the magnitude of
vector A
●B is the magnitude of
vector B
●?????? is the angle between
the two vectors
Use this formula to solve
for the scalar or dot
product of two vectors if
the magnitudes of both
vectors and the angle
between the vectors are
given.

41. Key Formulas


41
Concept Formula Description
Vector or Cross Product

where
●A is the magnitude of
vector A
●B is the magnitude of
vector B
●?????? is the angle between
the two vectors
Use this formula to solve
for the magnitude of the
vector product or cross
product of two vectors if
the magnitudes of both
vectors and the angle
between the vectors are
given.

42. Bibliography
42
Faughn, Jerry S. and Raymond A. Serway. Serway’s College Physics (7th ed). Singapore: Brooks/Cole, 2006.

Giancoli, Douglas C. Physics Principles with Applications (7th ed). USA: Pearson Education, 2014.

Knight, Randall D. Physics for Scientists and Engineers: A Strategic Approach (4th ed). USA: Pearson
Education, 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.