Free Printable Chapter 8: Vectors

1.

Two vectors are opposites if they have ____.

a)

the same magnitude and same direction

b)

different magnitudes and the same direction

c)

different magnitudes and opposite directions

d)

the same magnitude and opposite directions

2.

What is the magnitude of the resultant of a 100-newton force along the x-axis and a 150-newton force at an angle of 40° to each other?

a)

162.99 N

b)

180.28 N

c)

125 N

d)

235.54 N

3.

Find the magnitude of the resultant vector that is the sum of the two vectors shown.

a)

59

b)

165.2

c)

124

d)

80.1

4.

Find the initial horizontal velocity and vertical velocity of a stone kicked with an initial velocity of 15 feet per second at an angle of 42° with the ground.

a)

about 10 ft/s, about 22 ft/s

b)

about 14 ft/s, about 12 ft/s

c)

about 11 ft/s, about 10 ft/s

d)

about 11 ft/s, about 13 ft/s

5.

Write the component form of a vector with initial point X(–4, 7) and terminal point Y(3, –4)

a)

<-7, 11>

b)

<7, -11>

c)

<-1/2, 2/3>

d)

<2/3, -1/2>

6.

Find the magnitude of with initial point F(6, –3) and terminal point G(–2, 5).

a)

$12\sqrt{2}$

b)

$4\sqrt{5}$

c)

$2\sqrt{5}$

d)

$8\sqrt{2}$

7.

Find 3a - 2b + c for a = <3, -4>, b = <-1, 6>, and c = <2, 0>

a)

<9, 0>

b)

<9, -24>

c)

<12, -18>

d)

<13, -24>

8.

Find a unit vector u with the same direction as v = <4, -1>.

a)

$<\frac{4\sqrt{17}}{17},-\frac{\sqrt{17}}{17}>$

b)

$<\frac{4\sqrt{15}}{15},-\frac{\sqrt{15}}{15}>$

c)

$<\frac{4}{3},-\frac{1}{3}>$

d)

$<\frac{4\sqrt{7}}{7},-\frac{\sqrt{7}}{7}>$

9.

If José pushes a cart horizontally, exerting a horizontal force of 0.5 N up a 45° incline so that the cart moves 3 m, how much work has José done on the cart? A joule (J) is the SI unit for work or energy. 1 J = 1 N · 1 m

a)

$\frac{3\sqrt{2}}{2}J$

b)

$<\frac{3\sqrt{2}}{4},\ \frac{3\sqrt{2}}{2}>J$

c)

$\frac{3\sqrt{2}}{4}J$

d)

$<\frac{3\sqrt{2}}{4},\ \frac{3\sqrt{2}}{4}>J$

10.

Find the dot product of p and q if p = <2, -4> and q = <4, 7>.

a)

12

b)

-12

c)

20

d)

-20

11.

Which pair of vectors is orthogonal?

a)

$<4,\ 1>,\ <-8,\ 1>$

b)

$<5,\ 0>,\ <-3,\ 2>$

c)

$<5,\ -3>,\ <2,\ 3>$

d)

$<-9,\ -3>,\ <2,\ -6>$

12.

Use the dot product to find the magnitude of m = <10, - 4>.

a)

$2\sqrt{29}$

b)

36

c)

$2\sqrt{21}$

d)

196

13.

Which of the following diagrams corresponds to the point (–2, 3, –4)?

a)

b)

c)

d)

14.

Find the distance between points J(5, –1, 6) and K(–2, –7, –10).

a)

9.4

b)

18.5

c)

16.9

d)

19.2

15.

Find the midpoint between points R(6, 7, 5) and S(10, –9, –3).

a)

(8, 8, 1)

b)

(–2, –1, 1)

c)

(8, –1, 1)

d)

(–2, 8, 1)

16.

Which of the following vectors corresponds to the graph shown below?

a)

v = –3i + 4j + k

b)

v = 3i + 4j – k

c)

v = 3i – 4j – k

d)

v = –3i + 4j – k

17.

$Find\ \overrightarrow{c}\times\overrightarrow{d}\ if\ \overrightarrow{c}=<3,\ 0,\ -2>\ and\ \overrightarrow{d}=<-1,\ 3,\ 7>.$

a)

<-3, 0, -14>

b)

<-34, 0, -85>

c)

<2, 3, 5>

d)

<6, 19, 9>

18.

Find the dot product of a and b if a = <-4, 1, 2> and b = <3, 2, -1> .

a)

-8

b)

-12

c)

14

d)

-14

19.

Which pair of vectors is orthogonal?

a)

<1, 3, 1>, <0, 4, 2>

b)

<-2, 5, -4>, <3, 3, 6>

c)

<5, -1, -3>, <-2, -4, -2>

d)

<4, 3, 1>, <-1, 1, 2>

20.

Find the angle θ between u and v if u = <-2, 4, -5> and v = <6, -1, 3>.

a)

47.1º

b)

91.3º

c)

120.4º

d)

132.9º

Chapter 8: Vectors

Total questions: 20

Worksheet time: 10mins

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