The document discusses vectors and scalar quantities in statics. It defines scalars as having only magnitude, and vectors as having both magnitude and direction. Examples of scalars include mass and length, while examples of vectors include force and velocity. The document outlines objectives to define scalar and vector quantities and review common vector operations. It describes the parallelogram law for combining vectors and the principle of transmissibility for transmitting forces along their line of action. Polygon rules are presented for adding more than two vectors. Force systems and determining the resultant of vectors are also mentioned.

2. STATICS
(ENGINEERING MECHANICS-I)
Lecture #2
Vectors
December 22, 2022 GE 201: Dr. Fahed Alrshoudi 2
‫بسم‬
‫هللا‬
‫الرحمن‬
‫الرحيم‬
By

3. Contents
• Objective(s) of the present lecture (#2)
• Quantities: Scalars and Vectors
• Vector operations
December 22, 2022 GE 201: Dr. Fahed Alrshoudi 3

4. Objectives of the Present lecture
• To define scalar and vector quantities
• To provide an overview of most common
vector operations
December 22, 2022 GE 201: Dr. Fahed Alrshoudi 4

5. 1 - 5
ENGINEERING MECHANICS : STATICS
SCALAR QUANTITIES
A scalar is a quantity that has only magnitude,
either positive or negative.
For example; mass, length, area, volume and speed
are the scalar quantities frequently used in Statics.
Scalars are indicated by letters in Itallic type, such
as the scalar ‘A’.
Scalars and Vectors

6. 1 - 6
ENGINEERING MECHANICS : STATICS
VECTOR QUANTITIES
A vector is a quantity that has both a magnitude and a
direction.
For example; weight, force, moment, position, velocity and
acceleration are the vector quantities frequently used in Statics.
Vectors are indicated by bold letters, such as ‘A’ or A
The magnitude of a vector is always a positive quantity and is
symbolized in Itallic type, written as A or A
Scalars and Vectors

7. Scalars and Vectors
1 - 7
ENGINEERING MECHANICS : STATICS

8. 1- 8
Fundamental Principles – Paralellogram Law & Transmissibility
• Principle of Transmissibility
Conditions of equilibrium or motion are
not affected by transmitting a force
along its line of action.
NOTE: F and F’ are equivalent forces.
ENGINEERING MECHANICS : STATICS
Vectors must obey the parallelogram law of
combination. This law states that two vectors
A and B, treated as free vectors, may be replaced
by their equivalent vector (A+B), which is the
diagonal of the parelellogram formed by A and B
as its two sides, as shown in the figure.

10. P + Q + S = (P + Q) + S = P + (Q + S)
This is the Associative Law of Vector Addition
Polygon Rule:
can be used for the addition of more than two vectors. Two vectors are actually
summed and added to the third and so on...

13. CHAPTER 2 – FORCE SYSTEMS
(RESULTANT OF VECTORS)

14. 1 - 14
ENGINEERING MECHANICS : STATICS

15. 1 - 15
ENGINEERING MECHANICS : STATICS

16. 1 - 16
ENGINEERING MECHANICS : STATICS

17. 1 - 17
ENGINEERING MECHANICS : STATICS

18. 1 - 18
ENGINEERING MECHANICS : STATICS

19. 1 - 19
ENGINEERING MECHANICS : STATICS