Free Printable Unit 8 Vectors Review

Worksheets

Unit 8 Vectors Review

Total questions: 60

Worksheet time: 2hrs 57mins

Name

Class

Date

A vector is a ray with both ____________ and _____________.

Wings and halos

Space and time

Direction and magnitude

Radicals and exponents

Write in component form.

<0, 4>

<8, 2>

<2, 8>

<0, 2>

Find the resultant vector.

<5, 3>

<1, 7>

<7, 1>

<3, 5>

YARDWORK Nadia is pulling a tarp along level ground with a force of 25 pounds directed along the tarp. If the tarp makes an angle of 50° with the ground. Find the horizontal component of the force. Round to the nearest hundredth.

(a)

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 tenth.

(a)

Find the magnitude.

-4

Component Form

<-3, -7>

<3, -7>

<-3, 7>

<7, 3>

Find the resultant vector.

<-7, -1>

<5, 3>

<1, -9>

<8, 11>

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

2√3

2√17

2√15

2√5

10.

Calculate the component form of a vector with a magnitude: 422mph and a direction angle: 287°

< -403.6 , 123.4>

<123.4 , -403.6>

<123.4 , 403.6>

<-123.4 ,-403.6>

11.

Calculate the component form of the vector shown

< 63.9 , 44.7>

<7.3 , 34.2>

< -63.9 , 44.7>

<-7.3 , 34.2>

12.

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

<21, 2>

<-19, -13>

<-15, 3>

13.

Find the magnitude of the vector <-5, 12>

10.91

14.

Find the magnitude of vector AB if A is (-3, 1) and

B is (3, 9).

2√7

5√2

15.

If y = <2, 0> and z = <-1, -4>, find 3y - 2z

<5, -8>

<4, 8>

<8, 8>

<-8, -8>

16.

Determine the direction of <8, -2>

346 degrees

14 degrees

166 degrees

194 degrees

17.

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

161 degrees

-72 degrees

288 degrees

108 degrees

18.

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

<⅘, -⅗>

<0.57, -0.43>

<1, -1>

-¾

19.

Find a unit vector in the direction of <6, -8>

<0.6, -0.8>

<3, -4>

<1, -1>

<0, -2>

20.

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.

Direction 267.0°
Magnitude 485.6mph

Direction 93.0°
Magnitude 485.6mph

Direction 237.0°
Magnitude 485.6mph

Direction 87.0°
Magnitude 510.0mph

21.

Vector is a quantity with:

magnitude and direction

magnitude

direction

none of the above

22.

Does this statement describe a scalar quantity or a vector quantity?
Wind blowing West at 20 miles per hour

Scalar

Vector

23.

If a duck waddles from coordinate
P = (-3, 2) to
Q = (6,5), then a vector that models the duck's motion is

〈-3,7〉

〈-9,3〉

〈9,-3〉

〈9,3〉

24.

An airplane on course N15W° at 400 mph encounters a wind blowing 35 mph due east.
Find the vector w that represents the wind.

<35, 0>

<-35, 0>

<0, 35>

<0, -35>

25.

If v =〈a,b〉, then a is the ___________ component of v.

vertical

horizontal

parallel

slope

26.

An airplane on course N15W° at 400 mph encounters a wind blowing 35 mph due east.
Find the vector p that represents the plane.

400〈cos15i +sin15j〉

400〈cos105i +sin105j〉

400〈cos75i +sin75j〉

15〈cos400i +sin400j〉

27.

To find a position vector take

initial minus terminal

initial plus terminal

terminal minus initial

terminal plus initial

28.

Find the components of a vector v such that
v + 〈-6,4〉 = 〈10,-3〉

〈4,1〉

〈16,4〉

〈16,-7〉

none of these

29.

Which state does not exist in the USA?

South Dakota

North Dakota

Virginia

North Virginia

30.

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

They are parallel.

They are orthogonal.

They are neither.

31.

Find the ϴ between the vectors a = i + j and b = -2i + 3j.

180

11.31

78.69

71.57

32.

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

components

scalar

resultant

magnitude

33.

The scalar product of v and w

Dot product of v and w

vector v times vector w

V x W

34.

Find the component form of a vector whose magnitude is 10 and direction is 150°

<10,150>

<-8.66,5>

<6.99,-7.14>

<-10, 150>

35.

In Harry Potter, What is Hagrid's giant spider named?

Elfy

Aragog

Fang

Spider

36.

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

<-10,2>

<-6,10>

<4,-5>

<6,-10>

37.

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

<-11,26>

<8,3>

<21,2>

38.

Find the unit vector in the direction of <-7, 0>

-7

-1

<-1,0>

<1,0>

39.

Find the dot product of the given vectors:

-92

None og the above

40.

Where is Mount Rushmore?

North Dakota

South Dakota

North Carolina

South Carolina

41.

Find the magnitude.

-5

42.

Horizontal component

-18

-5

43.

Determine the components of the vector:

<5, 8.7>

<8.7, 5>

<59.1, 10.4>

<10.4, 59.1>

44.

Determine the direction of <8, -2>

346 degrees

14 degrees

166 degrees

194 degrees

45.

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

5408.2

26.3

689.8

73.5

46.

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

<3, -4>

<4, 0>

-1

47.

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

40.24°

49.76°

139.76°

92.57°

48.

How do you know if two vectors are orthogonal?

Their sum is 0.

The dot product is 1.

The angle between them is 0°.

The dot product is 0.

49.

Find the angle between u and v.

78.930^o

33.691^o

101.070^o

146.310^o

50.

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

〈14,-13〉

〈-14,13〉

〈-40,-21〉

〈40,-21〉

51.

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

Direction 21.3°
Magnitude 19.3

Direction 68.7°
Magnitude 19.3

Direction 21.3°
Magnitude 373

Direction 68.7°
Magnitude 373

52.

Find the angle between the vectors

142.13°

48.23°

261.24°

315.48°

53.

Find the angle between the vectors

142.13°

23.48°

132.88°

359.78°

54.

Find the angle between v and w

21.8 degrees

111.8 degrees

68.2 degrees

55.

Find the dot product if ||v||= 8, ||w||=6 and the angle between them is θ = 240˚

-24

-48

56.

Find the direction of vector <0, 4>.

180⁰

90⁰

270⁰

0⁰

57.

A unit vector is a vector that is _____________the given vector and has _____________.

parallel to, magnitude of 1

equal to, the same direction

opposite, the same size

smaller than, the same direction

58.

An arrow is shot at an angle of 35° from horizontal at a velocity of 140 feet per second. What is the horizontal (h) component of the velocity vector?

h = 114.68 fps

h = 140 fps

h = 80.30 fps

h = 105 fps

59.