Free Printable vectory!

1.

Vector is a quantity with:

a)

magnitude and direction

b)

magnitude

c)

direction

d)

none of the above

2.

a)

OB + BC = OC

b)

OA + AC = OC

c)

CB + B0 = -OC

d)

OD = 0.5(OA + AC)

3.

Vectors a, b, c are defined as:

a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers

a)

a + b = 3i + 8j

b)

a - b = i + 8j

c)

a + c = -i + 4j

d)

c - b = -5i + 6j

4.

Vector a = 2i + 3j - 5k. What is the value of 3a?

a)

3i + 3j - 3k

b)

5i + 6j - 8k

c)

6i + 9j -15k

d)

6i + 6j - 15k

5.

Find the magnitude.

a)

0

b)

5

c)

-5

d)

4

6.

Find the magnitude.

a)

5

b)

3

c)

25

d)

-4

7.

Find the magnitude.

a)

-10

b)

-8

c)

6

d)

10

8.

Component Form

a)

<-3, -7>

b)

<3, -7>

c)

<-3, 7>

d)

<7, 3>

9.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

10.

Horizontal component

a)

-18

b)

5

c)

18

d)

-5

11.

Find the resultant vector.

a)

<5, 3>

b)

<1, 7>

c)

<7, 1>

d)

<3, 5>

12.

Find the resultant vector.

a)

<9, 15>

b)

<7, 17>

c)

<15, 9>

d)

<11, 13>

13.

Find the resultant vector.

a)

<-10, 10>

b)

<10, -10>

c)

<15, 25>

d)

<25, 15>

14.

Find the resultant vector.

a)

<-7, -1>

b)

<5, 3>

c)

<1, -9>

d)

<8, 11>

15.

Magnitude

a)

Square root of 15

b)

Square root of 8

c)

4

d)

0

16.

Determine the components of the vector:

a)

<5, 8.7>

b)

<8.7, 5>

c)

<59.1, 10.4>

d)

<10.4, 59.1>

17.

Determine the components of the vector: magnitude= 12 and direction= 125 degrees

a)

< -9.9, 6.9 >

b)

< 9.9, -6.9 >

c)

< -6.9, 9.8 >

d)

< 6.9, -9.8 >

18.

Determine the magnitude of the vector <8, -2>

a)

2√3

b)

2√17

c)

2√15

d)

2√5

19.

Determine the direction of <8, -2>

a)

346 degrees

b)

14 degrees

c)

166 degrees

d)

194 degrees

20.

Determine the direction of the vector <-1, 3>

a)

161 degrees

b)

-72 degrees

c)

288 degrees

d)

108 degrees

21.

2 forces: 32N and 45 N with angle between of 35 deg. Determine the magnitude of the resultant.

a)

5408.2

b)

26.3

c)

689.8

d)

73.5

22.

2 forces 12N & 40N with angle between of 20 deg. Determine the magnitude of the resultant.

a)

51.4

b)

2646.1

c)

841.9

d)

29.0

23.

Find the direction of the vector <-3, -5>.

a)

59.03°

b)

239.03°

c)

210.96°

d)

120.96°

24.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

25.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

26.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

27.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

28.

Find the angle between u and v.

a)

78.930^o

b)

33.691^o

c)

101.070^o

d)

146.310^o

29.

Find the unit vector in the same direction as v.

a)

<0.385, 0.923>

b)

<-0.832, 0.555>

c)

<5/13, 12/13>

d)

<-5/13, -12/13>

30.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

31.

Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.

a)

〈-10,3〉

b)

〈-6,3〉

c)

〈10,11〉

d)

〈-6,-3〉

32.

Determine the direction and magnitude of the vector 〈-11,5〉

a)

Direction 24.4°
Vertical 12.1

b)

Direction65.6°
Magnitude 12.1

c)

Direction -24.4°
Magnitude 12.1

d)

Direction 155.6°
Magnitude 12.1

33.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

34.

Given u = <3, 7> and v =<-5, 4>, find 2u - 3v

a)

<21, 2>

b)

<-11, 26>

c)

<8, 3>

d)

23

35.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

36.

Find the magnitude of the vector <10, -8>

a)

2

b)

12.81

c)

6

d)

18

37.

Find the magnitude of the vector <5, 5>

a)

0

b)

10

c)

25

d)

7.07

38.

Find the direction angle for the vector <-8, 3>

a)

159.44°

b)

200.56°

c)

110.56°

d)

249.44°

39.

Find the unit vector in the direction of <4, -3>

a)

<⅘, -⅗>

b)

<0.57, -0.43>

c)

<1, -1>

d)

-¾

40.

A vector is a mathematical structure that has both _______ and _______.

a)

direction, magnitude

b)

scope, sequence

c)

meat, potatoes

d)

scalar, vector

41.

A car travels 90 meters due north in 15 seconds. Then the car turns around and travels 40 meters due south. What is the magnitude and direction of the car's resultant displacement?

a)

40 metres, South

b)

50 metres, South

c)

50 metres, North

d)

40 metres, North

42.

In practice A of the figure, What is the magnitude of the resultant displacement?

a)

5 km

b)

8 km

c)

11 km

d)

15 km

43.

In practice A of the figure, what is the direction of the resultant displacement?

a)

63 degrees, South of East

b)

63 degrees, North of West

c)

27 degrees, North of West

d)

27 degrees, South of West

44.

In practice B of the figure, which displacement is the horizontal component?

a)

30 km, East

b)

30 km, West

c)

40 km, North

d)

40 km, South

45.

Is this a scalar quantity or a vector quantity?
Wind blowing at 20 knots

a)

Scalar

b)

Vector

46.

Is this a scalar quantity or a vector quantity?
A deer running 15 meters per second due west

a)

Scalar

b)

Vector

47.

If a boomerang is thrown 20 m in a straight line and returns exactly to the spot it was thrown what is its displacement?

a)

20m

b)

40m

c)

0m

d)

-20m

48.

If a car moves 12 km North, 19 km East, and 12 km South, what is its displacement?

a)

12 km

b)

19 km, East

c)

31 km

d)

43 km, East

49.

Which of these is not a vector quantity?

a)

displacement

b)

time

c)

velocity

d)

acceleration

50.

The _______ of two or more vectors is the sum of the vectors.

a)

components

b)

scalar

c)

resultant

d)

magnitude

51.

What is the net force?
100 N 230 N
<------ --------->

a)

30 N to the right

b)

230 N to the right

c)

130 N to the right

d)

This is a balanced force

52.

Given the magnitude & direction of the resultant, find the horizontal & vertical components. Direction: 287° Magnitude: 422mph

a)

Horizontal -403.6
Vertical 123.4

b)

Horizontal 123.4
Vertical -403.6

c)

Horizontal 123.4
Vertical 403.6

d)

Horizontal -123.4
Vertical -403.6

53.

Given the magnitude & direction of the resultant, find the horizontal & vertical components.

a)

Horizontal 63.9
Vertical 44.7

b)

Horizontal 7.3
Vertical 34.2

c)

Horizontal -63.9
Vertical 44.7

d)

Horizontal -7.3
Vertical 34.2

54.

Given an initial point A ( 2, 4 ) and terminal point B ( -8, 7 ), find the component form of the vector AB.

a)

〈-10,3〉

b)

〈-6,3〉

c)

〈10,11〉

d)

〈-6,-3〉

55.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

56.

Determine the direction and magnitude of the vector 〈7,18〉

a)

Direction 21.3°
Magnitude 19.3

b)

Direction 68.7°
Magnitude 19.3

c)

Direction 21.3°
Magnitude 373

d)

Direction 68.7°
Magnitude 373

57.

Determine the direction and magnitude of the vector 〈-11,5〉

a)

Direction 24.4°
Vertical 12.1

b)

Direction65.6°
Magnitude 12.1

c)

Direction -24.4°
Magnitude 12.1

d)

Direction 155.6°
Magnitude 12.1

58.

Find the direction and magnitude of the resultant vector for the drawing of two forces.

a)

Direction 90°
Magnitude 139.0N

b)

Direction 52.3°
Magnitude 195N

c)

Direction 52.3°
Magnitude 139.0N

d)

Direction 37.7°
Magnitude 139.0N

59.

An airplane flying due south (270°) 485 mph against a 25 mph wind blowing due west(180°). Determine the new speed and direction of the plane.

a)

Direction 267.0°
Magnitude 485.6mph

b)

Direction 93.0°
Magnitude 485.6mph

c)

Direction 237.0°
Magnitude 485.6mph

d)

Direction 87.0°
Magnitude 510.0mph

60.

George Washington throws a baseball with an initial velocity of 20.2 feet per second at an angle of 69° with the horizontal. Find the initial vertical and horizontal velocity of the ball.

a)

Horizontal 18.9
Vertical 7.2

b)

Horizontal 7.2
Vertical 18.9

c)

Horizontal 15.2
Vertical 9.6

d)

Horizontal 9.6
Vertical 15.2

61.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

62.

Find the magnitude of vector AB if the initial point is (-3, 1) and the terminal point is (3, 9).

a)

6

b)

8.2

c)

10

d)

10.4

63.

Find the component form of vector AB with initial point A(0, 8) and terminal point B(-9, -3)

a)

<-9, 5>

b)

<-9, 11>

c)

<-9, -11>

d)

<-9, 5>

64.

If w = <2, -5> and y = <2, 0>, find 2w + y

a)

<-10, 2>

b)

<4, -5>

c)

<-6, 10>

d)

<6, -10>

65.

If R = (-2, 5) and S = (2, -8). Find the component form and magnitude of 4 times the resultant vector RS.

a)

<-15, 0> : 15

b)

<16, 52> : 54.4

c)

<-16, -52> : 42.5

d)

<16, -52> : 54.4

66.

Find the component form of a vector whose initial point is (5, 7) and terminal point is (1, 10)

a)

<-4, 3>

b)

<4, -3>

c)

5

d)

<6, 17>

67.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

68.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

69.

Find the angle between the two vectors:

a)

-0.789

b)

142.1

c)

100

d)

0.789

70.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

71.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

72.

Find the dot product of the given vectors:

a)

92

b)

0

c)

-92

d)

none of the above

73.

Find the angle between v and w

a)

21.8 degrees

b)

111.8 degrees

c)

68.2 degrees

74.

If the dot product of two vectors are equal to zero, then what do we know about the two vectors?

a)

They are parallel.

b)

They are orthogonal.

c)

They are neither.

75.

What type of quantity is produced by the dot product of two vectors?

a)

scalar

b)

vector

76.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

77.

Determine if the vectors are parallel, orthogonal, or neither. $<4,\ -2>$ and $<6,\ 12>$

a)

Parallel

b)

Orthogonal

c)

Neither

78.

Determine if the vectors are parallel, orthogonal, or neither.
$<4,\ -6>$ and $<-8,\ 12>$

a)

Parallel

b)

Orthogonal

c)

Neither

79.

Determine if the vectors are parallel, orthogonal, or neither.
$u\ =\ <4,\ -8>$ and $<0,\ -9>$

a)

Parallel

b)

Orthogonal

c)

Neither

80.

Given parallel vectors u and v. Answer ALL that apply

a)

their scalar product is zero

b)

their scalar product is either 1 or -1

c)

u is a scalar multiple of v

d)

magnitude of u equals the magnitude of v

81.

What operation you need to find an angle between two vectors?

a)

Dot product between the two vectors

b)

Dot product between the two vectors divide the magnitude of both vectors

c)

Cosine inverse of dot product between the two vectors divide the magnitude of both vectors

d)

Cross product between the two vectors

82.

What is the angle between two orthogonal vectors?

a)

180 degree

b)

90 degree

c)

60 degree

d)

45 degree

83.

Find the projection vector of u onto v. $u\ =\ <-6,\ -6>$ and $v\ =\ <-9,\ -3>$

a)

$<-7.2,\ -2.4>$

b)

$<3,\ 1>$

c)

$<-6.1,\ -2.3>$

d)

$<-9,\ -3>$

84.

Determine if the vectors are parallel, orthogonal, or neither. $<4,\ -2>$ and $<6,\ 12>$

a)

Parallel

b)

Orthogonal

c)

Neither

d)

Both

85.

Determine if the vectors are parallel, orthogonal, or neither.
$<4,\ -6>$ and $<-8,\ 12>$

a)

Parallel

b)

Orthogonal

c)

Neither

d)

Both

86.

Find the projection vector of u onto w. $u\ =\ <-1,\ 3>$ and $w\ =\ <2,\ -5>$

a)

$<-1.7,\ -5.1>$

b)

$<-5.1,\ -1.7>$

c)

$<-1.2,\ 2.9>$

d)

$<2.3,\ -4.9>$

87.

Determine if the vectors are parallel, orthogonal, or neither.
$u\ =\ <4,\ -8>$ and $<0,\ -9>$

a)

Parallel

b)

Orthogonal

c)

Neither

d)

Both

88.

Determine if the vectors are parallel, orthogonal, or neither. $u\ =\ 4i\ -\ j$ and $v\ =\ -3i\ -\ 12j$

a)

Parallel

b)

Orthogonal

c)

Neither

d)

Both

89.

Determine if the vectors are parallel, orthogonal, or neither. $u\ =\ -2i\ -9j$ and $v\ =\ -6i\ -\ 27j$

a)

Parallel

b)

Orthogonal

c)

Neither

d)

Both

90.

Find the projection of vector u onto w and then write vector u as the sum of two orthogonal vectors. $u\ =\ <1,\ 3>$ and $w\ =\ <2,\ 4>$

a)

$u\ =<1,\ 1>+<0,\ 2>$

b)

$u\ =\ <\frac{7}{5},\ \frac{14}{5}>+<-\frac{2}{5},\ \frac{1}{5}>$

c)

$u\ =\ <-\frac{189}{50},\ -\frac{27}{50}>+\ <\frac{239}{50},\ \frac{177}{50}>$

d)

$u\ =\ <-\frac{352}{65},\ -\frac{44}{65}>+<\frac{417}{65},\ \frac{239}{65}>$

91.

Find the projection of vector u onto v and then write vector u as the sum of two orthogonal vectors. $u\ =\ <8,\ 6>$ and $v\ =\ <4,\ 4>$

a)

$u\ =\ <1,\ -1>+<7,\ 7>$

b)

$u\ =<\frac{60}{13},\ \frac{40}{13}>+<\frac{34}{13},\ \frac{51}{13}>$

c)

$u\ =\ <\frac{63}{74},\ -\frac{45}{74}>+<-\frac{285}{74},\frac{399}{74}>$

d)

$u\ =\ <\frac{216}{89},\ \frac{135}{89}>+<\frac{140}{89},\ -\frac{224}{89}>$

92.

When finding the projection of vector u; u=〈3,2〉, onto vector v; v=〈5,-5〉 , which diagram illustrates this situation?

a)

b)

c)

d)

93.

When finding the projection of vector u; u=〈3,2〉, onto vector v; v=〈5,-5〉 $use\ w_1=\operatorname{proj}_vu=\frac{u\cdot v}{\parallel v\parallel^2}\cdot v$

a)

〈-½,½〉

b)

〈½,½〉

c)

〈½,-½〉

d)

〈-½,-½〉

e)

none of these

94.

After finding the projection of vector u; u=〈3,2〉, onto vector v; v=〈5,-5〉, find w₂.

a)

〈5/2,5/2〉

b)

〈-5/2,5/2〉

c)

〈5/2,-5/2〉

d)

〈-5/2,-5/2〉

95.

In a vector projection, w₁ and w₂ are referred to as the

____________________.

a)

proponets

b)

exponents

c)

donuts

d)

components

e)

hypotenuse

96.

If vector u is orthogonal to vector v, then the Proj_v u =

a)

1

b)

undefined

c)

infinity

d)

-1

e)

0

97.

if vector u and vector v are parallel or the same line, then Proj_v u =

a)

1

b)

-1

c)

u

d)

v

e)

0

98.

Find the projection of vector u onto v and then write vector u as the sum of two orthogonal vectors. $u\ =\ <8,\ 6>$ and $v\ =\ <4,\ 4>$

a)

$u\ =\ <1,\ -1>+<7,\ 7>$

b)

$u\ =<\frac{60}{13},\ \frac{40}{13}>+<\frac{34}{13},\ \frac{51}{13}>$

c)

$u\ =\ <\frac{63}{74},\ -\frac{45}{74}>+<-\frac{285}{74},\frac{399}{74}>$

d)

$u\ =\ <\frac{216}{89},\ \frac{135}{89}>+<\frac{140}{89},\ -\frac{224}{89}>$

99.

Find the projection of vector u onto w and then write vector u as the sum of two orthogonal vectors. $u\ =\ <1,\ 3>$ and $w\ =\ <2,\ 4>$

a)

$u\ =<1,\ 1>+<0,\ 2>$

b)

$u\ =\ <\frac{7}{5},\ \frac{14}{5}>+<-\frac{2}{5},\ \frac{1}{5}>$

c)

$u\ =\ <-\frac{189}{50},\ -\frac{27}{50}>+\ <\frac{239}{50},\ \frac{177}{50}>$

d)

$u\ =\ <-\frac{352}{65},\ -\frac{44}{65}>+<\frac{417}{65},\ \frac{239}{65}>$

100.

GARDENING Anne and Henry are lifting a stone statue and moving it to a new location in their garden. Anne is pushing the statue with a force of 120 newtons at a 60° angle with the horizontal while Henry is pulling the statue with a force of 180 newtons at a 40° angle with the horizontal. What is the magnitude of the combined force they exert on the statue? Round to the nearest hundredth.

(a)

101.

TRANSPORTATION A helicopter is moving 15° north of east with a velocity of 52 km/h. If a 30-kilometer per hour wind is blowing from a bearing of 250°, find the helicopter’s resulting velocity. Round to the nearest hundredth.

(a)

102.

Find a unit vector having the same distance as v. v = 11i + 60j

a)

v = (11/61)i + (60/61)j

b)

v = (11/49)i + (60/49)j

c)

v = (11/12)i + (60/12)j

d)

v = (11/65)i + (60/65)j

vectory!

Total questions: 102

Worksheet time: 5hrs 21mins

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