This document discusses force vectors and their properties. It defines vectors as quantities that have both magnitude and direction, while scalars only have magnitude. Vectors are represented graphically by arrows, with length indicating magnitude and angle indicating direction. Common vector quantities include displacement, velocity, and force. The document explains how to add, subtract, and resolve vectors into rectangular components using trigonometric or parallelogram methods. It also discusses resultant forces, Cartesian vectors, position vectors, forces directed along a line, and the dot product.

1. CHAPTER 2: FORCE VECTOR
2.1 Understand scalars and vectors
2.1.1 Differentiate between scalars and vectors

2. VECTORS SCALARS
• When comparing two vector
quantities of the same type, • For scalars, you only have
you have to compare both the to compare the
magnitude and the direction. magnitude.
When doing any
mathematical operation on a
vector quantity (like adding,
subtracting, multiplying ..)
you have to consider both the
magnitude and the direction.
This makes dealing with
vector quantities a little more
complicated than scalars.

3. • A vector is shown graphically by an arrow. The length of the
arrow represents the magnitude of the vector, and the angle
ᶿ between the vector and the fixed axis defines the direction
of its line of action. The head or tip of the arrow indicates the
sense of direction of the vector, Fig. 2-1

4. • Check Your Understanding
• 1. To test your understanding of this
distinction, consider the following quantities
listed below. Categorize each quantity as being
either a vector or a scalar.
– a. 5 m
– b. 30 m/sec, East
– c. 5 mi., North
– d. 20 degrees Celsius
– e. 256 bytes
– f. 4000 Calories

5. 2.1.2 Distinguish free vectors, sliding
vectors, fixed vectors

6. 2.2 Understand rectangular components
2.2.1 Explain two forces acting on a particle

7. 2.3 Understand vectors and vector operations
2.3.1 Calculate addition of vectors

9. 2.3.2 Calculate subtractions of vectors

10. 2.3.3 Determine resolutions of vectors
• The process of determining the magnitude of
a vector.
• The two methods of vector resolution that we
will examine are
– the parallelogram method
– the trigonometric method

11. The parallelogram method

12. The trigonometric method
The above method is illustrated below for determining the components of the
force acting upon Fido. As the 60-Newton tension force acts upward and
rightward on Fido at an angle of 40 degrees, the components of this force can
be determined using trigonometric functions.

13. 2.4 Understand the resultant force of
coplanar forces by addition

14. 2.5 Understand Cartesian vectors

15. 2.7 Understand position vectors
and x, y, z coordinates

16. 2.8 Understand the force vector
directed along the line

17. 2.9 Understand the dot product