Free Printable Chapter 8: Vectors Review

1.

Find the magnitude.

a)

5

b)

3

c)

25

d)

-4

2.

Find the magnitude.

a)

-10

b)

-8

c)

6

d)

10

3.

Component Form

a)

<-3, -7>

b)

<3, -7>

c)

<-3, 7>

d)

<7, 3>

4.

Write in component form.

a)

<0, 4>

b)

<8, 2>

c)

<2, 8>

d)

<0, 2>

5.

Horizontal component

a)

-18

b)

5

c)

18

d)

-5

6.

Find the resultant vector.

a)

<5, 3>

b)

<1, 7>

c)

<7, 1>

d)

<3, 5>

7.

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

8.

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

9.

Find a unit vector having the same distance as v. v = -4i - 3j

a)

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

b)

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

c)

v = (-4/25)i - (3/25)j

d)

v = (4/25)i + (3/25)j

10.

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

11.

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. What is the magnitude of the resultant?

(a)

12.

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)

13.

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)

14.

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)

15.

PHYSICS Janna is using a force of 100 pounds to push a cart up a ramp. The ramp is 6 feet long and is at a 30° angle with the horizontal. How much work is Janna doing in the vertical direction? (Hint: Use the sine ratio and the formula W = F ⋅ d.) Round to the nearest whole number.

(a)

16.

Find the projection vector of u onto v. $u=<-9,\ -5>$ and $v\ =\ <7,\ 1>$

a)

$<7,\ 1>$

b)

$<3.5,\ 0.5>$

c)

$<-9.5,\ -1.4>$

d)

$<-1,\ 7>$

17.

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)

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

18.

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)

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

19.

PHYSICS Suppose that the force acting on an object can be expressed by the vector 〈85, 35, 110〉, where each measure in the ordered triple represents the force in pounds. What is the magnitude of this force? Round to the nearest whole number.

(a)

20.

Find the volume of the parallelepiped with adjacent edges represented by the vectors 〈3, –2, 9〉, 〈6, –2, –7〉, and 〈–8, –5, –2〉 .

(a)

Chapter 8: Vectors Review

Total questions: 20

Worksheet time: 4hrs 30mins

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