This chapter discusses vectors, including the difference between scalar and vector quantities. Vectors are represented graphically using arrows proportional to magnitude and direction. Vector addition follows properties like commutativity and associativity. Resultant and equilibrant vectors are introduced. Methods for finding a resultant vector include graphical/polygon and analytical/component methods using trigonometry, rulers, and protractors. Examples demonstrate calculating magnitudes and directions of resultant vectors.

1. Chapter 2Vectors

2. In this chapter, we will discuss the following:the difference between scalar and vector quantities;representing vectors graphically;resultant and equilibrant vectors; and,finding resultant vector

3. Vectors and Scalars

4. Vectors and Scalars

5. Representing VectorsA vector is represented by an arrow.The length of the arrow is proportional to the magnitude of the vector.The tail indicates the starting point.The orientation of the arrowhead indicates the direction.Vectors maybe denoted using a boldface type (i.e. A denotes vector A).

6. Representing Vectors

7. Vector AdditionVector addition is different from the usual addition in arithmetic.The magnitude and direction should be taken into consideration.Only vectors of the same kind can be added or combined.

8. Properties of Vector AdditionCommutative : The order of addition does not matter.A + B = B + AAssociative : The grouping does not matter in adding 2 or more vectors.(A + B) + C = A + (B + C)

9. Resultant and Equilibrant

10. Finding Resultant VectorGraphical Method or Polygon MethodUse a ruler and a protractor.Analytical MethodRequires some knowledge in trigonometry.

11. Graphical / Polygon MethodDraw 1st vector using a convenient scale.From the terminal point (head) of the 1st vector, draw 2nd vector; from the terminal point (head) of the 2nd vector, draw 3rd vector; and so on, until the last vector.Draw the resultant vector (R) from the initial point (tail) of the 1st vector to the terminal point (head) of the last vector.Measure the resultant vector R using a ruler and a protractor to find its magnitude and direction.

12. Analytical / Component Method

13. Analytical / Component Method

14. Finding Resultant VectorAnswer: 950m East

15. Finding Resultant VectorAnswer: 300m West

16. Finding Resultant VectorAnswers : a. 7kmb. 5km, 53.13o N of E

17. Finding Resultant VectorAnswer : 6.17cm, 45.85o N of E

18. Solution for Example 40o0240o1.932.3090o02.54.304.43Direction:Magnitude:

19. Finding Resultant VectorAnswer : 15.80m, 29.71oN of W

20. Solution for Example 550o3.833.21150o4-6.93180o-100-13.727.83Direction:Magnitude:R = 15.8mθ = 150.29029.71o N of W

21. TRY THIS!!!