Free Printable MCV4U Vectors Unit 3

1.

Find the dot product of the given vectors:

a)

92

b)

0

c)

-92

d)

-120

2.

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

a)

They are parallel.

b)

They are perpendicular.

c)

They are unit vectors.

d)

They are both zero vectors.

3.

Find the angle between vectors (1,3) and (2,-5).

a)

40.2°

b)

49.7°

c)

139.7°

d)

92.6°

4.

Find the cross product of (3,4,7) and (4,9,2).

a)

(-55, 22, 11)

b)

(-55, -22, -9)

c)

(71,34, 63)

d)

(-71, -34, -630

5.

The cross product of vectors A and B is

a)

parallel to either A or B

b)

parallel to both A and B

c)

perpendicular to either A or B

d)

perpendicular to both A and B

6.

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

7.

Which vector operation is commutative?

a)

Dot Product

b)

Vector Projection

c)

Scalar Projection

d)

Cross Product

8.

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

a)

Parallel

b)

Perpendicular

c)

Neither

9.

Find the unit vector that has the same direction as the vector v.

v = 3i - 4j

a)

(3/5)i + (4/5)j

b)

(3/5)i - (4/5)j

c)

(4/5)i - (3/5)j

d)

(4/5)i + (3/5)j

10.

The magnitude of the vector product is __________.

a)

0

b)

1

c)

2

d)

3

11.

If they pull with a force of 200N for 10m, about how much work do they do?

a)

1700 J

b)

1800 J

c)

1900 J

d)

2000 J

12.

You pull your friend on a sled for 15 m at the angle provided and do 2600 J of work. What force did you exert?

a)

150

b)

175

c)

200

d)

225

13.

A wrench is used to tighten a nut. A 15N perpendicular force is applied 50cm away from the axis of rotation. What is the torque applied to the wrench?

a)

7.5 Nm

b)

1.5 Nm

c)

750 Nm

d)

150 Nm

14.

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

a)

i + 3j -5k

b)

-i -3j +3k

c)

i -j -5k

d)

-i -j +3k

15.

Given the vector v = 3i -2j +6 k, the magnitude of v is:

a)

36

b)

49

c)

7

d)

6

16.

A person pushes a car with a constant force of 120 N at a constant angle of 45 degree. Find the work done in Joules moving the car 10 meters.

a)

848.5 𝑗𝑜𝑢𝑙𝑒𝑠

b)

120 𝑗𝑜𝑢𝑙𝑒𝑠

c)

1200 𝑗𝑜𝑢𝑙𝑒𝑠

d)

130 𝑗𝑜𝑢𝑙𝑒𝑠

17.

Which of the following describes the vector above?

a)

45 cm

b)

45 cm at 30 degrees North of East

c)

45 cm at 30 degrees East of North

d)

45 cm North East

18.

A plane flies at 50 m/s west when it experiences a wind blowing north at 20 m/s. What is the resultant velocity of the plane?

a)

70 m/s at 22 degrees north of west

b)

54 m/s at 22 degrees north of west

c)

70 m/s at 22 degrees west of north

d)

54 m/s/ at 22 degrees west of north

19.

Given three vectors a, b and c as shown in the diagram. The best diagram for d = a - b + c is:

a)

b)

c)

d)

20.

Given the vector v = 3i -2j +6 k, the magnitude of v is:

a)

36

b)

49

c)

7

d)

6

21.

u + v

a)

4i - j

b)

6i + j

c)

3j + 4j

d)

i + 6j

22.

The cross product of vectors A and B is

a)

parallel to either A or B

b)

parallel to both A and B

c)

perpendicular to either A or B

d)

perpendicular to both A and B

23.

Which of the following is always positive?

a)

vector

b)

scalar

c)

direction

d)

magnitude

24.

What is the magnitude of : $\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}$

a)

1

b)

$\overrightarrow{0}$

c)

$\left|\overrightarrow{a}\right|$

d)

$\overrightarrow{a}$

25.

Velocity

a)

Vector

b)

Scalar

26.

Mass

a)

Vector

b)

Scalar

27.

Volume

a)

Vector

b)

Scalar

28.

Force

a)

Vector

b)

Scalar

29.

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

30.

What is the y component of the vector given in the diagram?

a)

77N

b)

92N

c)

120N

d)

60N

31.

What is the x component of the vector given in the diagram?

a)

77N

b)

92N

c)

120N

d)

60N

32.

How should you add two vectors? Select all that apply

a)

Add them head to tail

b)

Add them tail to tail

c)

don't why bother

d)

Use the parallelogram method

e)

Add them head to head

33.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS. Hint: get it into the pointy brackets.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

34.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

35.

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

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

36.

What is the sum of a vector addition problem called?

a)

components

b)

scalar

c)

resultant

d)

magnitude

37.

Convert $055\degree$ true bearing to its equivalent quadrant bearing

a)

$N55\degree E$

b)

$S55\degree E$

c)

$E55\degree N$

d)

$N55\degree W$

38.

Convert $230\degree$ true bearing to its equivalent quadrant bearing

a)

$S50\degree W$

b)

$N50\degree W$

c)

$S40\degree W$

d)

$S50\degree E$

39.

Convert $N30\degree W$ quadrant bearing to its true bearing

a)

$330\degree$

b)

$300\degree$

c)

$120\degree$

d)

$210\degree$

40.

Convert $S20\degree W$ quadrant bearing to its true bearing

a)

$200\degree$

b)

$20\degree$

c)

$-20\degree$

d)

$160\degree$

41.

1. Vectors $\overrightarrow{PQ}$ and $\overrightarrow{RS}$ are:

a)

parallel vectors

b)

opposite vectors

c)

equivalent vectors

d)

none

42.

1. Vectors $\overrightarrow{BA}$ and $\overrightarrow{CD}$ are:

a)

parallel vectors

b)

opposite vectors

c)

equivalent vectors

d)

equivalent and parallel

43.

1. Vectors $\overrightarrow{CB}$ and $\overrightarrow{AD}$ are:

a)

parallel vectors

b)

opposite vectors

c)

equivalent vectors

d)

opposite and parallel

44.

Simplify the following algebraically: $-2\overrightarrow{v}+0\overrightarrow{u}+2\overrightarrow{v}=$

a)

$\overrightarrow{0}$

b)

0

c)

$\overrightarrow{u}$

d)

$\overrightarrow{u}-\overrightarrow{v}$

45.

What is the magnitude of : $\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}$

a)

1

b)

$\overrightarrow{0}$

c)

$\left|\overrightarrow{a}\right|$

d)

$\overrightarrow{a}$

46.

Parallel vectors have the same magnitude but not necessarily the same direction

a)

True

b)

False

47.

Equivalent vectors have the same magnitude and direction.

a)

True

b)

False

48.

What vector is equivalent to $\overrightarrow{GA}$ ? Note that ACDG is a rectangle.

a)

$\overrightarrow{DC}$

b)

$\overrightarrow{CD}$

c)

$\overrightarrow{AB}$

d)

$-\overrightarrow{CE}$

49.

A rabbit leave his cave and hops 3 m [South] then 2 m [West]. How far, and in what direction, does the rabbit need to hop to return back to his cave?

a)

3.6 m [S34°W]

b)

3.6 m [N34°E]

c)

3.6 m [S56°W]

d)

3.6 m [N56°E]

50.

Which of these statements does NOT mean the same as the other three?

a)

$\overrightarrow{m}$ and $\overrightarrow{n}$ are parallel

b)

$\overrightarrow{m}$ and $\overrightarrow{n}$ are collinear

c)

$\overrightarrow{m}$ and $\overrightarrow{n}$ are scalar multiples of each other

d)

$\overrightarrow{m}$ and $\overrightarrow{n}$ are perpendicular to each other

51.

If $\left|\overrightarrow{a}\right|=7$ and $\left|\overrightarrow{b}\right|=3$ and the angle between the two vectors when lined up tail-to-tail is 90°, then what is $\left|\overrightarrow{a}-\overrightarrow{b}\right|$

a)

10.0

b)

7.6

c)

4.0

d)

6.3

52.

a)

$\overrightarrow{MP}$

b)

$\overrightarrow{PL}$

c)

$\overrightarrow{OP}$

d)

$\overrightarrow{NP}$

53.

Unit Vectors have a magnitude of one but no direction.

a)

True

b)

False

54.

If

\overrightarrow{a}=\left[1,\ 2\right]

and

\overrightarrow{b}=\left[2,\ 7\right]

find

\overrightarrow{a}+2\overrightarrow{b}

a)

$3\sqrt{10}$

b)

$[6,18]$

c)

$\left[5,\ 16\right]$

d)

$\sqrt{281}$

55.

If

\overrightarrow{m}=\left[-1,\ -1\right]

and

\overrightarrow{n}=\left[1,\ 1\right]

, find

\left|\overrightarrow{m}-\overrightarrow{n}\right|

a)

$\left[-2,\ -2\right]$

b)

$0$

c)

$\overrightarrow{0}$

d)

$2\sqrt{2}$

56.

Which vector is orthogonal to $\left[m,\ n\right]?$

a)

$\left[-m,\ -n\right]$

b)

$\left[n,\ m\right]$

c)

$\left[1,\ 1\right]$

d)

$[-n,m]$

57.

Stick person walked from home to school, then from the school to the park. What is their total displacement?

a)

2 km

b)

5 km

c)

8 km

d)

10 km

58.

Of $\overrightarrow{a}=\left[-10,-2,-4\right]$ , $\overrightarrow{b}=\left[3,-3,6\right]$ , and $\overrightarrow{c}=\left[5,1,-2\right]$ which two vectors are perpendicular?

a)

$\overrightarrow{a}$ and $\overrightarrow{b}$

b)

$\overrightarrow{c}$ and $\overrightarrow{b}$

c)

The Zero Vector and $\overrightarrow{c}$

d)

no two vectors are perpendicular

59.

If $\overrightarrow{a}=\left[1,2,3\right]$ and $\overrightarrow{b}=\left[3,2,1\right]$ , find $\overrightarrow{a}\cdot\overrightarrow{b}$ .

a)

[3,4,3]

b)

36

c)

10

d)

0

60.

A ship is on a heading of N10°W at 10 knots. Write this velocity as a Cartesian vector.

a)

$\overrightarrow{v}=\left[1.74,9.85\right]$

b)

$\overrightarrow{v}=\left[-1.74,9.85\right]$

c)

$\overrightarrow{v}=\left[1.74,-9.85\right]$

d)

$\overrightarrow{v}=\left[-1.74,-9.85\right]$

61.

A 10 N force is applied at 45° above the horizontal to the right. Write this force as a Cartesian vector.

a)

$\overrightarrow{F}=\left[10,\ 10\right]$

b)

$\overrightarrow{F}=\left[10,\ 0\right]$

c)

$\overrightarrow{F}=\left[\frac{10}{\sqrt{2}},\ \frac{10}{\sqrt{2}}\right]$

d)

$\overrightarrow{F}=\left[\frac{10}{\sqrt{2}},\ -\frac{10}{\sqrt{2}}\right]$

62.

Which vector is perpendicular with [m,n]?

a)

[-m,-n]

b)

[1,1]

c)

[n,m]

d)

[-n,m]

63.

Which vector is collinear with [a,b]?

a)

[b,a]

b)

[-a,b]

c)

[-a,-b]

d)

[b, -a]

64.

Which vector is collinear with [2, -3]?

a)

[2,-6]

b)

[12,18]

c)

[-2,-3]

d)

[-4,6]

65.

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

a)

components

b)

scalar

c)

resultant

d)

magnitude

66.

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

a)

<⅘, -⅗>

b)

<0.57, -0.43>

c)

<1, -1>

d)

-¾

67.

Which are equivalent vectors?

a)

u and -u

b)

u and a

c)

u and v

d)

u and b

68.

How should you add two vectors? Select all that apply

a)

Add them head to tail

b)

Add them tail to tail

c)

don't why bother

d)

Use the parallelogram method

e)

Add them head to head

69.

Given u = <3, 7>, find 2u

a)

<21, 2>

b)

<6, 26>

c)

<6, 14>

d)

23

70.

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

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

71.

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

72.

When adding two vectors graphically, a+b=c. Does b+a produce the same resultant vector c?

a)

Yes, two vectors added together always produce the same resultant vector

b)

No, because order matters

c)

Yes, but c will be pointing in the opposite direction

d)

No, because you can't add two vectors

73.

When subtracting two vectors, a-b=c. Does b-a produce the same resultant vector c?

a)

Yes, two vectors subtracted together always produce the same resultant vector

b)

No, because order matters

c)

Yes, but c will be pointing in the opposite direction

d)

No, because you can't subtract two vectors

74.

Which vector equation matches the vector operation shown in the diagram below?

a)

u + w = - v

b)

v + u = w

c)

w + u = v

d)

- v + w = 2u

75.

Find the angle between v and w. Round your answer to the nearest tenth.

v = -9i + 5j

w = -6i +9j

a)

3.7^o

b)

27.3^o

c)

37.3^o

d)

13.7^o

76.

Which of the following vectors are orthogonal to v = 12i - 6j?

a)

w = -6i + 12j

b)

w = 4i - 8j

c)

w = 4i + 8j

d)

w = 6i - 12j

MCV4U Vectors Unit 3

Total questions: 76

Worksheet time: 5hrs 19mins

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