Figure 1 Coordinate system

A is 6 m in length and points along the positive x-axis; vector B is 8 m in length and points along a direction 150° from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added?

a) 5 m 66.2⁰ north of west
b) 4.1 m 77.6⁰ north of west
c) 3.45 m 44.5⁰ north of west
d) 2.7 m 55⁰ north of west

11. 
    Vector A is 6 m in length and points along the positive x-axis. x-component of vector A is 2 m. Find the angle that vector A makes with respect to x-axis.
    

a) 19°
b) 45°
c) 60°
d) 71°

12. 
    Five force vectors act on an object. The magnitude of each force is 20 N. Each force points in a different direction: north, northeast, east, southeast, and south. The angle between each vector is 45⁰. Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?
    

a) 44.22 N
b) 31.12 N
c) 28.28 N
d) 55.55 N

13. 
    Given two vectors A = 7.0i - 2.0j and B = 15.0i + 9.0j? What are the magnitude and direction of A + B?
    

a) 23 m 17.65⁰ north of east
b) 17 m 25.6⁰ north of east
c) 29 m 14.10⁰ south of east
d) 33 m 55⁰ north of west

14. 
    Given the two displacements:
    

Find the magnitude of the displacement
a) 22.35 m b) 29.75 m c) 35.41 m d) 41.23 m

15. 
    If A = 2C +B, B = 4C -A and C = 6i + 8j, then what are a and b?
    

1. 
   
   
2. 
   
   
3. 
   
   
4. 
   
   

1. 
   Given a vector . Find the angle with respect to the positive x-axis.
   

1. 
   53.13⁰ b) 155.16⁰ c) 126.87⁰ d) 140.23⁰
   

1. 
   Given two vectors . What is the scalar product of two vectors?
   

1. 
   3 b) 5 c) 7 d) 10
   

18. 
    Find the angle between
    

a) 8.21⁰ b) 7.53⁰ c) 4.91⁰ d) 6.03⁰

19. 
    Two vectors are given by and . Find the vector product of these two vectors and direction.
    

a) -22 b) -36 c) 30 d) 43

20. 
    Given and . What is the vector product and direction?
    

a) 19 b) -36 c) 30 d) 34

21. 
    Vector lies on positive x-axis and has a magnitude of 8 m. Vector has a magnitude of 6 m and makes an angle of 60⁰ with respect to positive x-axis. What is the vector product of these two vectors?
    

a) 41.56 b) 35.21 c) 51.25 d) 49.23

22. 
    Calculate , if you are given the vector with the magnitude of 8 m and angle it makes with respect to positive x-axis is 30⁰, the vector has magnitude of 6 m and an angle the vector makes with positive x-axis is 55⁰ and the vector with magnitude 3 m and points in the positive z-direction.
    

a) 55.16 b) 42.31 c) 60.85 d) 70.2

23. 
    Three vectors are presented as , , . Find
    

a) b)
c) d)

23. 
    

    Figure 2.45

    Figure 2.46

    In the triangle shown in the figure, the side lengths are a = 8 cm, b = 18.5 cm, and c = 11.3 cm. What is the value of the angle ? (Hint: Use the law of cosines.)
    

a) 31.25⁰ b) 19.95⁰ c) 24.32⁰ d) 31.24⁰
25. Find the unknown side of the triangle shown in Figure 2.46.
a) 18.52 b) 10.23 c) 11.24 d) 14.73

1. 
   

Test - 1
1	B	6	C	11	D	16	C	21	A
2	B	7	B	12	C	17	A	22	C
3	C	8	D	13	A	18	C	23	A
4	D	9	A	14	B	19	B	24	B
5	A	10	B	15	D	20	D	25	D