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How to Write a Paragraph


Paragraph writing remains one of the most important parts of writing. The paragraph serves as a container for each of the ideas of an essay or other piece of writing. Paragraphs are versatile and can take many forms that strengthen your writing, provide variety for readers, and help readers to organize the ideas you present.

Paragraph Length in a Piece of Writing

While it is true that a paragraph may be of any length, it is most common for an essay paragraph to be at least 3-5 sentences long and to be no longer than half a typed, double-spaced page. Journalism paragraphs (newspapers and magazines) tend to be 1-3 sentences long. Some paragraphs in books, especially technical treatises, might go on for several printed pages.
No matter what length an individual paragraph, most good writing varies paragraph length within any one piece of writing. If there are a few short paragraphs, then a longer one usually comes along. If there are one or two long paragraphs, usually a short paragraph or two will intervene to give the reader a short break in concentration.

Use Paragraphs to Break Up Ideas

A paragraph is the container for only one idea. Often, a longer paragraph can - and should - be divided into smaller units. Usually a large, complex idea is made up of smaller ideas and can be explained in more paragraphs with those smaller ideas. The point, though, is to have one coherent paragraph - all of the ideas in each sentence of the paragraph must relate to a single main point. That point is most often made in a topic sentence.

Topic Sentences in Paragraphs

A topic sentence gives the main idea of a paragraph. It usually occurs as the first or last sentence of the paragraph. Some paragraphs will not have a topic sentence, if the main point is obvious. Others might place the topic sentence slightly differently. Occasionally, as in this paragraph, the topic sentence might begin the paragraph but be restated in a different way at the end. That is to say, most writers put the topic sentence of a paragraph at the beginning or the end or both.

Grammar in Paragraphs

Every sentence in a paragraph must be grammatically correct, in so much as that grammar aids in understanding the ideas that the writer would like to convey. The topic sentence, in particular, must be very well written and very clear to readers. Of course, WhiteSmoke's grammar checker can be employed here to pick up any errors. The WhiteSmoke free online grammar checker could even be used if you just need to check your writing very occasionally.

Types of Paragraphs

Most writing has an introductory paragraph or an introduction of a few paragraphs, and a conclusion of a few paragraphs or concluding paragraph. The introduction and conclusion are, of course, supported by body paragraphs. The typical body paragraph develops, supports, or elaborates a given topic sentence. Most paragraph structures longer than 1-2 sentences have common elements.

For example, expository paragraphs have three important elements common to most paragraphs: flow, or unity (a clear connection to the rest of the essay and placed in a sensible way among the other paragraphs; development (detailed, specific support or elaboration of the main idea); and coherence (each sentence clearly relates to the previous and next sentence in an understandable and sensible manner). Persuasive paragraphs focus on developing a strong argument that would convince someone who disagrees with the writer's position.
Narrative paragraphs have similar features of flow (or unity) and coherence. However, the development might be more related to the action or events narrated in the paragraph than to supporting an argument. Coherence in a narrative paragraph usually comes from the chronological order of the "story" or narrative. Similarly, a descriptive paragraph might find its development through giving a series of sensory details or of abstract ideas that describe an object (or concept or theory), rather than through support. These two types of paragraph - narrative and descriptive - differ only slightly in these respects from expository paragraphs, but the differences are still important.
With some attention to flow, development, and coherence in your paragraphs, you will soon be writing powerfully.

How to Make Paragraph

Jumat, 28 November 2014
Posted by Mella

Career Planning Tips


Building a Career

Today, and more than ever, most people are responsible for building their own careers.
Whether you are just starting, or you have several years of experience, these paragraphs might help you advance your career.
The 9 most important career planning tips is listed below:

1. Never Stop Learning

Life-long learning is your keyword.
The world is constantly changing, and everybody is looking for new ways of doing business.
If you have decided that your current skills are good enough, you have also decided that your current job is good enough.
But if you want a career in the future, you should add regular updates to your skills and knowledge.

2. Ask, Listen And Learn

A good listener can learn a lot.
Listen to your co-workers, your boss, and your superiors. You can learn a lot from their experience.
Ask about issues that interest you, and listen to what they say. Let them tell you about how things work, and what you could have done better.
Most people will love to be your free tutor.

3. Fulfill Your Current Job

Your current job might be best place to start your career.
It is often very little that separates successful people from the average. But nothing comes free.
If you do your job well and fulfill your responsibilities, this is often the best way to start a new career.
Talk to your supervisor about things you can do. Suggest improvements. Offer your help when help is needed. In return ask for help to build a better career. It is often possible - right inside your own organization - especially if you have proved to be a valued employee.

4. Build Your Network

Your next career step might arise from your contact network.
Did you know that more than 50% of all jobs are obtained from contact networks?
If you have a good contact network, it  is also a good place to discover future careers, to explore new trends, and to learn about new  opportunities.
Spend some time building new contacts, and don't forget to maintain the ones you already have.
One of the best ways to get serious information from your network is to regularly ask your contacts how they are, what they do, and what is new about their careers.

5. Identify Your Current Job

Your current job should be identified, not assumed.
Make sure you don't work with tasks you assume are important. This is waste of time and talent.
When you start in a new job, talk to your superior about your priorities. If you're not sure about what is most important, then ask him. And ask him again. Often you will be surprised about the differences between what you assume, and what is really important.

6. Identify Your Next Job

Your dream job must be identified.
Before you start planning your future career, be sure you have identified your dream job.
In your dream job, you will be doing all the things you enjoy, and none of the things you don't enjoy. What kind of job would that be?
Do you like or dislike having responsibility for other employees. Do you like to work with technology or with people? Do you want to run your own business? Do you want to be an artist, a designer or a skilled engineer? A manager?
Before building your future career your goal must be identified.

7. Prepare Yourself

Your dream might show up tomorrow. Be prepared.
Don't wait a second. Update your CV now, and continue to update it regularly.
Tomorrow your dream job may show up right before your nose. Prepare for it with a professional CV and be ready to describe yourself as a valuable object to anyone that will try to recruit you.
If you don't know how to write a CV, or how to describe yourself, start learning it now.

8. Pick The Right Tools

Pick the tools you can handle.
You can build your future career using a lot of different tools. Studying at W3Schools is easy. Taking a full master degree is more complicated.
You can add a lot to your career by studying books and tutorials (like the one you find at W3Schools). Doing short time courses with certification tests might add valuable weight to your CV. And don't forget: Your current job is often the most valuable source of building new skills.
Don't pick a tool that is too heavy for you to handle!  

9. Realize Your Dreams

Put your dreams into action.
Don't let a busy job kill your dreams. If you have higher goals, put them into action now.
If you have plans about taking more education, getting a better job, starting your own company or something else, you should not use your daily job as a "waiting station". Your daily job will get more and more busy, you will be caught up in the rat race, and you will burn up your energy.
If you have this energy, you should use it now, to realize your dreams.

Learn About Job

Posted by Mella

Unit 4 - Lesson 17 - Telling the Time in English # 2

Remember

Revise these time expressions - Telling the time # 1

Learn

Requires Real Player Basic

Telling the time to the half hour or quarter hour

There are 15 minutes in quarter of an hour.
There are 30 minutes in half an hour.
There are 45 minutes in three quarters of an hour.
When it's past the hour (up to 30 minutes past) we say "past".
When it's before the hour (after 30 minutes past) we say "to".
30 minutes is half an hour, we say "half past" or "thirty".
15 minutes is quarter of an hour. At 15 minutes past the hour we say "quarter past" or "fifteen". At fifteen minutes to the hour we say "quarter to" or "forty-five".
Clock Face
Telling the time Twelve o'clock Telling the time Twelve fifteen

or

Quarter past twelve
Telling the time Twelve thirty

or

Half past twelve
Telling the time Twelve forty-five

or

Quarter to one
!Note - you don't mention the "minutes".

Naturally speaking

Exactly or about

Exactly About
14.00
It's exactly two o'clock.
14.28
It's about half past two.
How to ask the time - requires Real Player Basic
Telling the time
  • It's exactly eight o'clock.

or
  • It's eight.
Telling the time
  • It's half past twelve.

or
  • It's twelve thirty.
Telling the time
  • It's about half past eleven.

or
  • It's about eleven thirty.

Writing the time

AM 00:01 - 11:59
write a.m. - stands for Ante Meridiem (the time between midnight and noon) 00:01 to 11:59
write noon or midday 12:00
write p.m. - stands for Post Meridian (after noon) 12:01 - 23:59
write midnight 24:00

Speaking about the time generally

If you say "Good morning" at 1 am, people will think you are strange. Different rules apply, which are more to do with how light it is. See also "Greetings".
Daytime - the time between sunrise and sunset Starts at sunrise / dawn
morning - the time between sunrise and noon sunrise - 11:59
afternoon - the time between noon and sunset 12:01 - sunset
Nighttime - the time between sunset and sunrise Starts at sunset / dusk
evening - the time between sunset and night (full darkness) sunset - darkness
night - the time after evening and before sunrise dark - sunrise

There are 24 hours in a day, but only the military, police and computer programmers use the 24-hour clock. When writing or speaking generally we tend to use the 12-hour clock.
The 24 hours of the day are divided into two periods called a.m. (Latin "ante meridiem" | English: "before mid day") and p.m. (Latin "post meridiem" | English: "after mid day").
The way people write the time varies. I prefer a.m. and p.m.
Choose from the following styles or use what your English teacher tells you to and stick to it:-
a.m. p.m.
am pm
AM PM
A.M. P.M.
Some people use a dot as the separator: 2.30 pm.
Some people use a colon as the separator: 2:30 pm. The colon is usually used with the 24-hour clock: 14:30.

Learn About Time

Posted by Mella
Adjectives Describing People and Personal Qualities Vocabulary Word List More Adjectives
More Word Banks
A
able
abnormal
absent-minded
above average
adventurous
affectionate
agile
agreeable
alert
amazing
ambitious
amiable
amusing
analytical
angelic
apathetic
apprehensive
ardent
artificial
artistic
assertive
attentive
average
awesome
awful
B
balanced
beautiful
below average
beneficent
blue
blunt
boisterous
brave
bright
brilliant
buff
C
callous
candid
cantankerous
capable
careful
careless
caustic
cautious
charming
childish
childlike
cheerful
chic
churlish
circumspect
civil
clean
clever
clumsy
coherent
cold
competent
composed
conceited
condescending
confident
confused
conscientious
considerate
content
cool
cool-headed
cooperative
cordial
courageous
cowardly
crabby
crafty
cranky
crass
critical
cruel
curious
cynical
D
dainty
decisive
deep
deferential
deft
delicate
demonic
dependent
delightful
demure
depressed
devoted
dextrous
diligent
direct
dirty
disagreeable
discerning
discreet
disruptive
distant
distraught
distrustful
dowdy
dramatic
dreary
drowsy
drugged
drunk
dull
dutiful
E
eager
earnest
easy-going
efficient
egotistical
elfin
emotional
energetic
enterprising
enthusiastic
evasive
even-tempered
exacting
excellent
excitable
experienced
F
fabulous
fastidious
ferocious
fervent
fiery
flabby
flaky
flashy
frank
friendly
funny
fussy
G
generous
gentle
gloomy
glutinous
good
grave
great
groggy
grouchy
guarded
H
hateful
hearty
helpful
hesitant
hot-headed
hypercritical
hysterical
I
idiotic
idle
illogical
imaginative
immature
immodest
impatient
imperturbable
impetuous
impractical
impressionable
impressive
impulsive
inactive
incisive
incompetent
inconsiderate
inconsistent
independent
indiscreet
indolent
indefatigable
industrious
inexperienced
insensitive
inspiring
intelligent
interesting
intolerant
inventive
irascible
irritable
irritating
J
jocular
jovial
joyous
judgmental
K
keen
kind
L
lame
lazy
lean
leery
lethargic
level-headed
listless
lithe
lively
local
logical
long-winded
lovable
love-lorn
lovely
M
maternal
mature
mean
meddlesome
mercurial
methodical
meticulous
mild
miserable
modest
moronic
morose
motivated
musical
N
naive
nasty
natural
naughty
negative
nervous
noisy
normal
nosy
numb
O
obliging
obnoxious
old-fashioned
one-sided
orderly
ostentatious
outgoing
outspoken
P
passionate
passive
paternal
paternalistic
patient
peaceful
peevish
pensive
persevering
persnickety
petulant
picky
plain
plain-speaking
playful
pleasant
plucky
polite
popular
positive
powerful
practical
prejudiced
pretty
proficient
proud
provocative
prudent
punctual
Q
quarrelsome
querulous
quick
quick-tempered
quiet
R
realistic
reassuring
reclusive
reliable
reluctant
resentful
reserved
resigned
resourceful
respected
respectful
responsible
restless
revered
ridiculous
S
sad
sassy
saucy
sedate
self-assured
selfish
sensible
sensitive
sentimental
serene
serious
sharp
short-tempered
shrewd
shy
silly
sincere
sleepy
slight
sloppy
slothful
slovenly
slow
smart
snazzy
sneering
snobby
somber
sober
sophisticated
soulful
soulless
sour
spirited
spiteful
stable
staid
steady
stern
stoic
striking
strong
stupid
sturdy
subtle
sullen
sulky
supercilious
superficial
surly
suspicious
sweet
T
tactful
tactless
talented
testy
thinking
thoughtful
thoughtless
timid
tired
tolerant
touchy
tranquil
U
ugly
unaffected
unbalanced
uncertain
uncooperative
undependable
unemotional
unfriendly
unguarded
unhelpful
unimaginative
unmotivated
unpleasant
unpopular
unreliable
unsophisticated
unstable
unsure
unthinking
unwilling
V
venal
versatile
vigilant
W
warm
warmhearted
wary
watchful
weak
well-behaved
well-developed
well-intentioned
well-respected
well-rounded
willing
wonderful
Y
volcanic
vulnerable
Z
zealous
More Word Lists
Adjectives
Adverbs
Alliteration
Amphibians
Anagrams
Animals
Antonyms
April Fool's Day
Art
Astronomy
Autumn/Fall
Backyard
Baseball
Bathroom
Beach
"Big"
Birds
Biomes
Birthday
Boats/Ships
Bodies of Waters
Body
Buildings
Business and Office
Camping
Carnivals and Fairs
Car Parts
Cars
Castles, Kings, Queens
Cats
Chinese New Year
Christmas (secular)
Circus and Carnival
Clothing
Colors
Columbus Day
Compound Words
Computers
Constitution
Conjunctions
Containers
Cooking Terms
Cooking Tools
Country Names
Dance
Dentist
Desserts
Dogs
Doctors and Dentists
Dolch Words
Driving
Duos
Elections
Elements
Emotions and Feelings
Energy
Fall/Autumn
Family
Farm
Fire Fighting
Fish
Flowers
Food
Food Web
Friends, Acquaintances, and Other People
Fruit
Furniture
Geography
Good Luck Symbols
Grammar
Groundhog Day
Halloween
Happiness
"Happy" synonyms
Hats
Herbs and Spices
Holidays
House
Household Devices
Housing and Dwellings
Insects
Interjections
Irregular Verbs
Jobs and Occupations
Kitchen
Landforms
Languages
Leaders
Legal Terms
Long E Words
Long U Words
Mammals
"Many"
Martin Luther King, Jr.
Math and Numbers
Measurement
Metals
Military
Money
Monsters
Mother's Day
Musical Instruments
Music Theory
New Year's Eve
Negative Words
Nouns that are Verbs
Ocean
Office and Business
Opposites
Pairs
Palindromes
People (Non-Family)
Personal Qualities
Pirates
Plants
Positive Words
Post Office
Prepositions
President's Day
Pronouns
Regular Verbs
Reptiles
Restaurant
Roadways
Rocks and Minerals
Rooms
"Said"
School
Science
Science Fields
Sewing
Shapes
Ships/Boats
Shoes
Spices and Herbs
Sports
Spring
Stores and Public Buildings
Summer
St. Patrick's Day
Thanksgiving
Time
Tools
Transportation and Vehicles
Trees
Types of Cars
US Constitution
US Flag Day
US States
Vacation
Valentine's Day
Vegetables
Vehicles and Transportation
Verbs
Verbs, Irregular
Verbs, Regular
Verbs that are Nouns
Virtues
Water
Ways to Say "Big"
Ways to Say "Happy"
Ways to Say "Many"
Ways to Say "Said"
Weapons
Weather
Weights and Measures
Winter
Yard

    1. 60s-inspired
    2. 70s-inspired
    3. 80s-inspired
    4. active
    5. adjustable
    6. adorable
    7. anatomic
    8. anatomically designed
    9. antimicrobial
    10. asymmetrical
    11. banded
    12. beaded
    13. beautiful
    14. big & tall
    15. bloused
    16. bold
    17. boot cut
    18. boxy
    19. boys'
    20. breathable
    21. button-down
    22. buttoned
    23. casual
    24. chic
    25. classic
    26. collared
    27. colored
    28. colorful
    29. comfortable
    30. comfy
    31. constructed of
    32. contemporary
    33. control-top
    34. cool
    35. couture
    36. crisp
    37. cross-stitched
    38. cushioned
    39. custom
    40. cut-out
    41. cute
    42. cutting-edge
    43. dainty
    44. dapper
    45. decorative
    46. dependable
    47. designer
    48. detailed
    49. discounted
    50. distressed
    51. dramatic
    52. drapey
    53. durable
    54. easy-to-maintain
    55. eco-friendly
    56. edgy
    57. efficient
    58. elegant
    59. embellished
    60. embroidered
    61. engineered
    62. environmentally-friendly
    63. ergonomic
    64. essential
    65. everyday
    66. exceptional
    67. exciting
    68. exotic
    69. extra large
    70. fabric-lined
    71. fancy
    72. fashionable
    73. faux
    74. favorite
    75. feminine
    76. figure-friendly
    77. finely detailed
    1. flattering
    2. flexible
    3. flirty
    4. floaty
    5. forgiving
    6. form-fitting
    7. full-priced
    8. fully lined
    9. funky
    10. geometric
    11. girls'
    12. glamorous
    13. glitzy
    14. graceful
    15. half-priced
    16. hand-sewn
    17. hand-washed
    18. handsome
    19. high-performance
    20. high-waisted
    21. hot
    22. imported
    23. individualist
    24. innovative
    25. intricate
    26. itch-free
    27. junior's
    28. kids'
    29. knit
    30. lacy
    31. lapel
    32. large
    33. latest
    34. layered
    35. lightweight
    36. line-free
    37. lined
    38. long-lasting
    39. loose
    40. machine washable
    41. masculine
    42. medium
    43. men's
    44. metallic
    45. mini
    46. minimalist
    47. mixed-media
    48. modern
    49. moisture-wicking
    50. must-have
    51. non-iron
    52. odor-absorbing
    53. odor-resistant
    54. old-fashioned
    55. opaque
    56. organic
    57. oversized
    58. patchwork
    59. patterned
    60. petite
    61. pieced
    62. pleated
    63. plus size
    64. plush
    65. polished
    66. practical
    67. premium
    68. preppy
    69. pretty
    70. printed
    71. professional
    72. protective
    73. pull-on
    74. quilted
    75. racy
    76. refined
    77. reflective
    1. reinforced
    2. relaxed
    3. reliable
    4. remodeled
    5. retro
    6. retro print
    7. reworked
    8. ribbed
    9. ripstop
    10. rocker-style
    11. romantic
    12. ruched
    13. rugged
    14. sale-priced
    15. sassy
    16. savvy
    17. scooped-neck
    18. see-through
    19. sensational
    20. sexy
    21. shaping
    22. sheer
    23. short sleeve
    24. silky
    25. silky soft
    26. simple
    27. skinny
    28. skinny-fit
    29. sleek
    30. slimmer
    31. slimming
    32. slip-on
    33. slouched
    34. slouchy
    35. small
    36. soft
    37. solid
    38. sophisticated
    39. sporty
    40. standard
    41. standard-fit
    42. state-of-the-art
    43. stitched
    44. straight
    45. strapless
    46. stretch
    47. stretchy
    48. structural
    49. stunning
    50. stylish
    51. superior
    52. supersoft
    53. supple
    54. supportive
    55. symmetrical
    56. synthetic
    57. tailored
    58. textured
    59. tight
    60. timeless
    61. top-of-the-line
    62. translucent
    63. trendsetting
    64. trendy
    65. true-to-size
    66. unique
    67. versatile
    68. vintage
    69. voluminous
    70. waist-slimming
    71. water-resistant
    72. waterproof
    73. wear-anywhere
    74. whimsical
    75. women's
    76. yarn-dyed
    77. zippered
    heloww...learning reading yukss, open this link http://downloads.ziddu.com/download/24218426/reading-power-ok.pdf.html

    Vectors and Direction

    A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories - vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions.
    Examples of vector quantities that have been previously discussed include displacement, velocity, acceleration, and force. Each of these quantities are unique in that a full description of the quantity demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you "A bag of gold is located outside the classroom. To find it, displace yourself 20 meters." This statement may provide yourself enough information to pique your interest; yet, there is not enough information included in the statement to find the bag of gold. The displacement required to find the bag of gold has not been fully described. On the other hand, suppose your teacher tells you "A bag of gold is located outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north." This statement now provides a complete description of the displacement vector - it lists both magnitude (20 meters) and direction (30 degrees to the west of north) relative to a reference or starting position (the center of the classroom door). Vector quantities are not fully described unless both magnitude and direction are listed.


    Representing Vectors

    Vector quantities are often represented by scaled vector diagrams. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction. Vector diagrams were introduced and used in earlier units to depict the forces acting upon an object. Such diagrams are commonly called as free-body diagrams. An example of a scaled vector diagram is shown in the diagram at the right. The vector diagram depicts a displacement vector. Observe that there are several characteristics of this diagram that make it an appropriately drawn vector diagram.
    • a scale is clearly listed
    • a vector arrow (with arrowhead) is drawn in a specified direction. The vector arrow has a head and a tail.
    • the magnitude and direction of the vector is clearly labeled. In this case, the diagram shows the magnitude is 20 m and the direction is (30 degrees West of North).


    Conventions for Describing Directions of Vectors

    Vectors can be directed due East, due West, due South, and due North. But some vectors are directed northeast (at a 45 degree angle); and some vectors are even directed northeast, yet more north than east. Thus, there is a clear need for some form of a convention for identifying the direction of a vector that is not due East, due West, due South, or due North. There are a variety of conventions for describing the direction of any vector. The two conventions that will be discussed and used in this unit are described below:
    1. The direction of a vector is often expressed as an angle of rotation of the vector about its "tail" from east, west, north, or south. For example, a vector can be said to have a direction of 40 degrees North of West (meaning a vector pointing West has been rotated 40 degrees towards the northerly direction) of 65 degrees East of South (meaning a vector pointing South has been rotated 65 degrees towards the easterly direction).
    2. The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about its "tail" from due East. Using this convention, a vector with a direction of 30 degrees is a vector that has been rotated 30 degrees in a counterclockwise direction relative to due east. A vector with a direction of 160 degrees is a vector that has been rotated 160 degrees in a counterclockwise direction relative to due east. A vector with a direction of 270 degrees is a vector that has been rotated 270 degrees in a counterclockwise direction relative to due east. This is one of the most common conventions for the direction of a vector and will be utilized throughout this unit.

    Two illustrations of the second convention (discussed above) for identifying the direction of a vector are shown below.
    Observe in the first example that the vector is said to have a direction of 40 degrees. You can think of this direction as follows: suppose a vector pointing East had its tail pinned down and then the vector was rotated an angle of 40 degrees in the counterclockwise direction. Observe in the second example that the vector is said to have a direction of 240 degrees. This means that the tail of the vector was pinned down and the vector was rotated an angle of 240 degrees in the counterclockwise direction beginning from due east. A rotation of 240 degrees is equivalent to rotating the vector through two quadrants (180 degrees) and then an additional 60 degrees into the third quadrant.


    Representing the Magnitude of a Vector

    The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn a precise length in accordance with a chosen scale. For example, the diagram at the right shows a vector with a magnitude of 20 miles. Since the scale used for constructing the diagram is 1 cm = 5 miles, the vector arrow is drawn with a length of 4 cm. That is, 4 cm x (5 miles/1 cm) = 20 miles.
    Using the same scale (1 cm = 5 miles), a displacement vector that is 15 miles will be represented by a vector arrow that is 3 cm in length. Similarly, a 25-mile displacement vector is represented by a 5-cm long vector arrow. And finally, an 18-mile displacement vector is represented by a 3.6-cm long arrow. See the examples shown below.



    In conclusion, vectors can be represented by use of a scaled vector diagram. On such a diagram, a vector arrow is drawn to represent the vector. The arrow has an obvious tail and arrowhead. The magnitude of a vector is represented by the length of the arrow. A scale is indicated (such as, 1 cm = 5 miles) and the arrow is drawn the proper length according to the chosen scale. The arrow points in the precise direction. Directions are described by the use of some convention. The most common convention is that the direction of a vector is the counterclockwise angle of rotation which that vector makes with respect to due East.

    In the remainder of this lesson, in the entire unit, and in future units, scaled vector diagrams and the above convention for the direction of a vector will be frequently used to describe motion and solve problems concerning motion. For this reason, it is critical that you have a comfortable understanding of the means of representing and describing vector quantities. Some practice problems are available on site at the following web page:

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