VECTORS WORKSHEETS
pg 1 of 13
VECTORS
Objectives
Students will be able to:
1
Define Sine, Cosine and Tangent in terms of the opposite, adjacent and hypotenuse of a triangle.
2
Use the above trig functions to finds angles and right triangle side lengths.
3
Define a vector in a sentence.
4
Describe a vector’s two main features.
5
Define a scalar in a sentence.
6
Give examples of vectors and scalars.
7
Be able to identify if two vectors are equal
8
Graphically show the result of multiplying a vector by a positive scalar.
9
Graphically show the result of multiplying a vector by a negative scalar.
10 Graphically add vectors.
11 Graphically subtract vectors.
12 Graphically add, subtract and multiply vectors by a scalar in one equation.
13 Given a graphical representation of a vector equation, come up with the formula.
14 Calculate the magnitude of any vector’s horizontal and vertical components.
15 Draw a vector’s horizontal and vertical components.
16 Use trig to calculate a vector’s direction.
17 Calculate a vectors direction as a degree measurement combined with compass directions.
18 Calculate a vector’s magnitude using trig or Pythagorean theorem.
19 Add and subtract vectors by their components.
VECTORS WORKSHEETS
pg 2 of 13
SECTION 1
A
2A
1A
2
B
-4C
D
C
- 1D
2
A + B = R1
SECTION 2
A + 4C = R 2
A + 2B + 1 C = R 3
2
A - C = R4
SECTION 3
B - A = R5
2C - B = R 6
2C - A - B = R 7
For the vectors below, calculate the vector’s magnitude, and direction.
SECTION 4
VECTORS WORKSHEETS
pg 3 of 13
For each vector drawn below on a coordinate axis, label the shown θ with it proper compass headings,
e.g. N of W, S, S of E, etc.
1
2
3
θ
8
4
5
6
θ
θ
θ
7
θ
θ
9
10
θ
θ
11
12
13
14
θ
θ
θ
15
θ
16
17
18
19
θ
22
20
23
24
21
θ
θ
θ
θ
θ
θ
θ
θ
24
θ
26
27
28
θ
θ
θ
θ
θ
θ
29
30
31
32
33
θ
38
39
θ
θ
θ
θ
37
θ
35
θ
θ
θ
36
34
40
41
θ
θ
θ
42
θ
θ
43
44
45
θ
46
47
θ
48
θ
49
θ
50
θ
θ
θ
51
52
θ
53
θ
θ
54
θ
55
56
θ
θ
θ
VECTORS WORKSHEETS
pg 4 of 13
For each vector drawn below, calculate its magnitude and direction. NOTE: For the vector’s direction, there
will be two possible correct answers for each problem. The two answers are complimentary to each
other.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24
26
27
28
29
30
31
32
33
34
35
θ
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
VECTORS WORKSHEETS
VECTORS - GRAPHICAL MEANS
FIND THE RESULATANTS, (R#):
A + B = R1 , B + C = R2 , E + D = R3 , A - B = R4 , B - D = R5 , E - C = R6 ,
A + B + D = R7 , E + A + C = R8 , A + (-B) = R9 , -B + C + (-D) = R1 0 ,
E - A + C - D = R1 1 ,
pg 5 of 13
VECTORS WORKSHEETS
pg 6 of 13
Adding by Vector Componants
1
2
15 m/s
10 m/s
8 m/s
25°
55°
40°
8 m/s
10°
3
4
40°
44°
8m
3N
33°
10 m
7N
VECTORS WORKSHEETS
pg 7 of 13
Adding by Vector Componants
5
6
10 m/s
15 m/s
6N
35°
72°
50°
50°
3N
20°
10 N
8 m/s
7
8
9 m/s 2
8 m/s 2
10 m/s
15°
5 m/s
50°
13 m/s
43°
4 m/s
8 m/s 2
VECTORS WORKSHEETS
pg 8 of 13
Basic Math by Vector Componants
FIND THE RESULATANT’S LENGTH AND ACUTE ANGLE WITH THE HORIZONTAL FOR
EACH R#:
A + B = R1 , B + C = R2 , E + D = R3 , A - B = R4 , B - D = R5 , E - C = R6 ,
A + B + D = R7 , E + A + C = R8 , A + (-B) = R9 , -B + C + (-D) = R1 0 ,
E - A + C - D = R1 1 ,
A
13.6
4
θ =17.1
B
C
12
D
26.57 = θ
8.94
26.57 = θ
E
Vector
R1
R2
R3
R4
R5
R6
R7
R8
R9
R10
Magnitude
2 √17 =8.25
2 √13 = 7.21
√5 = 2.24
2 √41 = 12.81
17
11
1
17
2 √41 = 12.81
2 √13 = 7.21
7
Direction
OR
18.43° N of E
56.31° N of W
63.43° S of W
38.66° W of S
28.07° N of E
Due East
Due West
14.04° E of S
38.66° W of S
56.31° W of S
Direction
71.57° E of N
33.69° W of N
26.57° W of S
51.34° S of W
61.93° E of N
------75.96° S of E
51.34° S of W
33.69° S of W
θ = 26.57
VECTORS WORKSHEETS
pg 9 of 13
Find the missing variable
28°
A
x
8°
40
x
10
C
15° 8
x
40°
D
B
10
x
8
E
30
H
x
F
35°
45°
3
x
x
G
12°
x
25°
9
55° 15
K
1.5
x
I
24°
12
J
68°
x
x
x
N
62°
70°
375
x
x
L
0.70
O
37
115
M
55°
x
49°
x
21°
P
1.5
Q
x
53°
352
VECTORS WORKSHEETS
pg 10 of 13
Find the angle θ
θ
A
4
10
30
8
B
60 θ
40
C
θ
D
θ
10
3
8
E
30
40
θ
12
F
θ
θ
3
H
θ
2
40
G
9
15
K
1.5
40
θ
I
12
J
30
0.6
θ
θ
16
N
375
θ
0.55
500
0.70
L
85
M
O
37
115
θ
θ
θ
1
Q
P
θ
1.5
435
352
θ
VECTORS WORKSHEETS
pg 11 of 13
Find the missing variable
A
33°
A
10
52
9
B
50
C
C
D
41°
θ
10
θ
3
E
53°
110
H
E
59.6
73°
G
102
F
45°
0.025
G
250
θ
F
θ
K
J 23°
38
54°
I
18
12
J
I
0.2
14
N
37
θ
L
L
O
25
6005
0.058
θ
700
0
M
66
θ
73
°
71
P
94
θ
Q
9.5
57°
Q
VECTORS WORKSHEETS
pg 12 of 13
A
- 1D
2A
2A
2
1A
2
B
-4C
D
C
1A
2
-4C
- 1D
2
A + B = R1
A
B
A + 4C = R 2
A + 2B + 1 C = R 3
1/2 C
2
4C
A
2B
A
A - C = R4
A
B - A = R5
C
B
A
2C - B = R 6
B
2C - A - B = R 7
A
2 C -A
2C
B
A
B
2 C -A
2C
2C
For the vectors below, calculate the vector’s magnitude, and direction.
mag = 5.00
θ = DUE SOUTH
mag = 9.90
θ = 45 N of E
mag = 8.49
θ = 45 S of E
mag = 7.07
θ = 45 N of E
mag = 7.28
θ = 15.95 E of S
θ = 74.05 S of E
mag = 10.00
θ = 53.13 N of E
θ = 36.87 E of N
VECTORS WORKSHEETS
pg 13 of 13
R1
R2
R3
R4
R5
R6
R7
R9
R8
R10
R11
ANSWERS