## Scalars

Physical quantities which can be completely specified by

1. A number which represents the magnitude of the quantity.

2. An appropriate unit

are called Scalars.

Scalars quantities can be added, subtracted multiplied and divided by usual algebraic laws.

**Examples**

Mass, distance, volume, density, time, speed, temperature, energy, work, potential, entropy, charge etc.

## Vectors

Physical quantities which can be completely specified by

1. A number which represents the magnitude of the quantity.

2. An specific direction

are called Vectors.

Special laws are employed for their mutual operation.

**Examples**

Displacement, force, velocity, acceleration, momentum.

**Representation of a Vector**

A straight line parallel to the direction of the given vector used to represent it. Length of the line on a certain scale specifies the magnitude of the vector. An arrow head is put at one end of the line to indicate the direction of the given vector.

The tail end O is regarded as *initial point* of vector R and the head P is regarded as the *terminal point* of the vector R.

**Unit Vector**

A vector whose magnitude is unity (1) and directed along the direction of a given vector, is called the unit vector of the given vector.

A unit vector is usually denoted by a letter with a cap over it. For example if r is the given vector, then r will be the unit vector in the direction of r such that

r = r .r

**Or**

r = r / r

unit vector = vector / magnitude of the vector

**Equal Vectors**

Two vectors having same directions, magnitude and unit are called equal vectors.

**Zero or Null Vector**

A vector having zero magnitude and whose initial and terminal points are same is called a null vector. It is usually denoted by O. The difference of two equal vectors (same vector) is represented by a null vector.

R - R - O

**Free Vector**

A vector which can be displaced parallel to itself and applied at any point, is known as free vector. It can be specified by giving its magnitude and any two of the angles between the vector and the coordinate axes. In 3-D, it is determined by its three projections on x, y, z-axes.

**Position Vector**

A vector drawn from the origin to a distinct point in space is called position vector, since it determines the position of a point P relative to a fixed point O (origin). It is usually denoted by r. If xi, yi, zk be the x, y, z components of the position vector r, then

r = xi + yj + zk

**Negative of a Vector**

The vector A. is called the negative of the vector A, if it has same magnitude but opposite direction as that of A. The angle between a vector and its negative vector is always of 180º.

**Multiplication of a Vector by a Number**

When a vector is multiplied by a positive number the magnitude of the vector is multiplied by that number. However, direction of the vector remain same. When a vector is multiplied by a negative number, the magnitude of the vector is multiplied by that number. However, direction of a vector becomes opposite. If a vector is multiplied by zero, the result will be a null vector.

The multiplication of a vector A by two number (m, n) is governed by the following rules.

1. m A = A m

2. m (n A) = (mn) A

3. (m + n) A = mA + nA

4. m(A + B) = mA + mB

**Division of a Vector by a Number (Non-Zero)**

If a vector A is divided by a number n, then it means it is multiplied by the reciprocal of that number i.e. 1/n. The new vector which is obtained by this division has a magnitude 1/n times of A. The direction will be same if n is positive and the direction will be opposite if n is negative.

## Resolution of a Vector Into Rectangular Components

**Definition**

Splitting up a single vector into its rectangular components is called the Resolution of a vector.

**Rectangular Components**

Components of a vector making an angle of 90º with each other are called rectangular components.

**Procedure**

Let us consider a vector F represented by OA, making an angle O with the horizontal direction.

Draw perpendicular AB and AC from point on X and Y axes respectively. Vectors OB and OC represented by Fx and Fy are known as the rectangular components of F. From head to tail rule of vector addition.

OA = OB + BA

F = Fx + Fy

To find the magnitude of Fx and Fy, consider the right angled triangle OBA.

Fx / F = Cos θ => Fx = F cos θ

Fy / F = sin θ => Fy = F sin θ

**Addition of Vectors by Rectangular Components**

Consider two vectors A1 and A2 making angles θ1 and θ2 with x-axis respectively as shown in figure. A1 and A2 are added by using head to tail rule to give the resultant vector A.

The addition of two vectors A1 and A2 mentioned in the above figure, consists of following four steps.

**Step 1**

For the x-components of A, we add the x-components of A1 and A2 which are A1x and A2x. If the x-components of A is denoted by Ax then

Ax = A1x + A2x

Taking magnitudes only

Ax = A1x + A2x

**Or**

Ax = A1 cos θ1 + A2 cos θ2 ................. (1)

**Step 2**

For the y-components of A, we add the y-components of A1 and A2 which are A1y and A2y. If the y-components of A is denoted by Ay then

Ay = A1y + A2y

Taking magnitudes only

Ay = A1y + A2y

**Or**

Ay = A1 sin θ1 + A2 sin θ2 ................. (2)

**Step 3**

Substituting the value of Ax and Ay from equations (1) and (2) respectively in equation (3) below, we get the magnitude of the resultant A

A = |A| = √ (Ax)2 + (Ay)2 .................. (3)

**Step 4**

By applying the trigonometric ratio of tangent θ on triangle OAB, we can find the direction of the resultant vector A i.e. angle θ which A makes with the positive x-axis.

tan θ = Ay / Ax

θ = tan-1 [Ay / Ax]

Here four cases arise

(a) If Ax and Ay are both positive, then

θ = tan-1 |Ay / Ax|

(b) If Ax is negative and Ay is positive, then

θ = 180º - tan-1 |Ay / Ax|

(c) If Ax is positive and Ay is negative, then

θ = 360º - tan-1 |Ay / Ax|

(d) If Ax and Ay are both negative, then

θ = 180º + tan-1 |Ay / Ax|

## Addition of Vectors by Law of Parallelogram

According to the law of parallelogram of addition of vectors, if we are given two vectors. A1 and A2 starting at a common point O, represented by OA and OB respectively in figure, then their resultant is represented by OC, where OC is the diagonal of the parallelogram having OA and OB as its adjacent sides.

If R is the resultant of A1 and A2, then

R = A1 + A2

**Or**

OC = OA + OB

But OB = AC

Therefore,

OC = OA + AC

β is the angle opposites to the resultant.

Magnitude of the resultant can be determined by using the law of cosines.

R = |R| = √A1(2) + A2(2) - 2 A1 A2 cos β

Direction of R can be determined by using the Law of sines.

A1 / sin γ = A2 / sin α = R / sin β

This completely determines the resultant vector R.

**Properties of Vector Addition**

*1. Commutative Law of Vector Addition (A+B = B+A)*

Consider two vectors A and B as shown in figure. From figure

OA + AC = OC

**Or**

A + B = R .................... (1)

And

OB + BC = OC

**Or**

B + A = R ..................... (2)

Since A + B and B + A, both equal to R, therefore

A + B = B + A

Therefore, vector addition is commutative.

*2. Associative Law of Vector Addition (A + B) + C = A + (B + C)*

Consider three vectors A, B and C as shown in figure. From figure using head - to - tail rule.

OQ + QS = OS

**Or**

(A + B) + C = R

And

OP + PS = OS

**Or**

A + (B + C) = R

Hence

(A + B) + C = A + (B + C)

Therefore, vector addition is associative.

**Product of Two Vectors**

1. Scalar Product (Dot Product)

2. Vector Product (Cross Product)

**1. Scalar Product OR Dot Product**

If the product of two vectors is a scalar quantity, then the product itself is known as Scalar Product or Dot Product.

The dot product of two vectors A and B having angle θ between them may be defined as the product of magnitudes of A and B and the cosine of the angle θ.

A . B = |A| |B| cos θ

A . B = A B cos θ

Because a dot (.) is used between the vectors to write their scalar product, therefore, it is also called dot product.

The scalar product of vector A and vector B is equal to the magnitude, A, of vector A times the projection of vector B onto the direction of A.

If B(A) is the projection of vector B onto the direction of A, then according to the definition of dot product.

A . B = A B(A)

A . B = A B cos θ {since B(A) = B cos θ}

Examples of dot product are

W = F . d

P = F . V

**Commutative Law for Dot Product (A.B = B.A)**

If the order of two vectors are changed then it will not affect the dot product. This law is known as commutative law for dot product.

A . B = B . A

if A and B are two vectors having an angle θ between then, then their dot product A.B is the product of magnitude of A, *A*, and the projection of vector B onto the direction of vector i.e., B(A).

And B.A is the product of magnitude of B, *B*, and the projection of vector A onto the direction vector B i.e. A(B).

To obtain the projection of a vector on the other, a perpendicular is dropped from the first vector on the second such that a right angled triangle is obtained

In Δ PQR,

cos θ = A(B) / A => A(B) = A cos θ

In Δ ABC,

cos θ = B(A) / B => B(A) = B cos θ

Therefore,

A . B = A B(A) = A B cos θ

B . A = B A (B) = B A cos θ

A B cos θ = B A cos θ

A . B = B . A

Thus scalar product is commutative.

**Distributive Law for Dot Product**

A . (B + C) = A . B + A . C

Consider three vectors A, B and C.

B(A) = Projection of B on A

C(A) = Projection of C on A

(B + C)A = Projection of (B + C) on A

Therefore

A . (B + C) = A [(B + C}A] {since A . B = A B(A)}

= A [B(A) + C(A)] {since (B + C)A = B(A) + C(A)}

= A B(A) + A C(A)

= A . B + A . C

Therefore,

B(A) = B cos θ => A B(A) = A B cos θ1 = A . B

And C(A) = C cos θ => A C(A) = A C cos θ2 = A . C

Thus dot product obeys distributive law.

**2. Vector Product OR Cross Product**

When the product of two vectors is another vector perpendicular to the plane formed by the multiplying vectors, the product is then called vector or cross product.

The cross product of two vector A and B having angle θ between them may be defined as "the product of magnitude of A and B and the sine of the angle θ, such that the product vector has a direction perpendicular to the plane containing A and B and points in the direction in which right handed screw advances when it is rotated from A to B through smaller angle between the positive direction of A and B".

A x B = |A| |B| sin θ u

Where u is the unit vector perpendicular to the plane containing A and B and points in the direction in which right handed screw advances when it is rotated from A to B through smaller angle between the positive direction of A and B.

Examples of vector products are

(a) The moment M of a force about a point O is defined as

M = R x F

Where R is a vector joining the point O to the initial point of F.

(b) Force experienced F by an electric charge q which is moving with velocity V in a magnetic field B

F = q (V x B)

**Physical Interpretation of Vector OR Cross Product**

Area of Parallelogram = |A x B|

Area of Triangle = 1/2 |A x B|

This comment has been removed by a blog administrator.

ReplyDeletenumerical number 10 of this chapter

ReplyDeleteit would be more helpful if u add diagrams as well..

ReplyDeleteThis blog is gud but try to improve it by helping diagrams and examples thanx

ReplyDeletegood notes I like it

ReplyDeleteWhat’s Going down i am new to this, I stumbled upon this

ReplyDeleteI've found It

absolutely helpful and it has helped me out loads. I am hoping to give a

contribution & assist different customers like its aided me. Good

job.

Stop by my page:2012 us open 9 ball videoI’ve read a few good stuff here. Definitely worth bookmarking for revisiting.

ReplyDeleteI

wonder how much effort you put to make such a wonderful

informative site.

Feel free to visit my web page:spanier surnameHi, Neat post. There is a problem with your website in internet explorer, would check

ReplyDeletethis… IE still is the market leader and a huge portion of people will miss your magnificent writing due to this problem.

My web blog...http://www.costablancaspain.us/weather-climate.HtmlHello.This post was really interesting, especially

ReplyDeletesince I was investigating for thoughts on this matter last

Friday.

Here is my site...http://bootstrapsandlawyers.blogspot.ru/I savor, cause I found just what I used to be looking for.

ReplyDeleteYou've ended my 4 day long hunt! God Bless you man. Have a great day. Bye

Also see my website>hotels in madrid spain in gran avenidaAs I web-site possessor I believe the content material here

ReplyDeleteis rattling magnificent , appreciate it for your hard work.

You should keep it up forever! Good Luck.

Review my web page::mw.propl.euThank you so much for providing individuals with an

ReplyDeleteexceptionally remarkable opportunity to discover

important secrets from this site. It's always

very terrific plus packed with a lot of fun for me and my office

acquaintances to search your web site at the least three times every week to find out the newest tips you will have. And of course,

we're usually

motivated with your unique thoughts you serve. Some two areas on this page are really the

most impressive I've ever had.

Review my site;blogspot.ruI love your blog.. very nice colors & theme. Did you make this website yourself or did you

ReplyDeletehire someone to do it for you? Plz answer back as I'm looking to create my own blog and

would like to find out where u got this from. thank you

Here is my weblog;www.chris-ensoll.comHmm is anyone else encountering problems with the pictures on this blog

ReplyDeleteloading? I'm trying

to figure out if its a problem on my end or if it's the blog.

Any responses would be greatly appreciated.

Here is my web site::http://inside-geography.blogspot.fr/2012/12/thailand.htmlCan I just say what a aid to find somebody who

ReplyDeletereally knows what theyre speaking about on the internet.

You positively know methods to bring a problem to

mild and make it important. More individuals need to read this

and perceive this facet of the story. I cant believe youre no more

widespread because you definitely have the gift.

Also visit my blog post::http://wearemudlark.com/derby2061/index.php?title=Live_The_Dream_With_VW_Campervan_Hire_SpainThanks , I've just been looking for info about this

ReplyDeletesubject for ages and yours is the best I have discovered till now. But, what about the

bottom line? Are you sure about the source?

My webpage-123facebook.comThanks , I've just been looking for information about this

ReplyDeletesubject for ages and yours is the greatest I've discovered

so far. But, what about the

conclusion? Are you sure about the source?

Here is my webpage...demo.pacifichost.comHmm it looks like your site ate my first

ReplyDeletecomment (it was extremely long) so I guess

I'll just sum it up what I had written and say, I'm thoroughly enjoying your

blog. I as well am an

aspiring blog writer but I'm still new to the whole thing. Do you have any tips and hints for inexperienced blog

writers? I'd definitely appreciate it.

My web site-10 day weather Forecast alcudiaHello! I just would like to give a huge thumbs

ReplyDeleteup for the nice information you will have here on this post.

I will probably be coming back to your blog for extra soon.

My web page-2012 Nba Mock Draft 2011I would like to thank you for the efforts you've put in writing this site. I

ReplyDeleteam hoping the same high-grade blog post from you in the upcoming also. In fact your creative writing abilities has inspired me to get my own web site

now. Really the blogging is spreading its wings fast. Your write up is a great

example of it.

Check out my webpage:2011 world series game 4 box scoreI don’t even know how I ended up here, but I thought this post was good.

ReplyDeleteI do not know who you are

but certainly you're going to a famous blogger if you aren't already

;) Cheers!

my webpage::Solar Powered Swimming Pool HeatingExceptional post however , I was

ReplyDeletewanting to know if you could write a litte more on this subject?

I'd be very thankful if you

could elaborate a little bit further. Kudos!

Also see my web page:diysolarheatingspain.comhey there and thank you for your information - I have

ReplyDeletedefinitely picked up something new from right here.

I did however experience a few technical issues using

this website, as I experienced to reload the site a lot of instances prior

to I could get it to load properly. I

were pondering in case

your web hosting is OK? No longer that I'm complaining, but sluggish loading instances occasions will often affect your placement in google and can damage your quality ranking if advertising and ***********

Also visit my homepage;www.sffp.asso.frWhat i do not understood is actually how you are not actually much more

ReplyDeletewell-liked than

you might be right now. You're very intelligent. You realize therefore

considerably relating to this subject, made me personally consider it from so many varied angles. Its like men and women aren't fascinated unless it is one thing to

accomplish with Lady gaga! Your own stuffs

great. Always maintain it up!

Review my blog...einstein-university.orgnaturally like your website however you have

ReplyDeleteto test the spelling on several of your posts. A number of them are rife

with

spelling problems and I in finding it very troublesome to inform the

truth nevertheless I’ll certainly come

again again.

Look at my blog post:http://whoisstuff.net/Great blog right here! Additionally your site rather

ReplyDeletea lot up very fast! What web host are you using? Can

I am getting your affiliate link on your host? I want my website loaded up as quickly as yours lol

Review my siteblogspot.ruDefinitely believe that that you said. Your

ReplyDeletefavorite reason seemed to be on the web the

simplest factor to have in mind of. I say to you, I definitely get annoyed even as other

folks consider worries that they just do not recognize about.

You controlled to hit the nail upon the top and also defined out the entire thing without having side-effects , folks could take

a signal. Will probably be back to get more.

Thanks

Here is my weblog::weirdquietgirl.blogspot.ruThanks a lot for sharing this with all of us you actually know what you're talking about!

ReplyDeleteBookmarked. Please also visit my web site =). We could have a link exchange

arrangement between us!

Look into my blog post;http://www.natashafatah.com/2012/01/basils-first-snow.htmlWoah! I'm really enjoying the template/theme of this site. It's

ReplyDeletesimple, yet effective. A

lot of times it's very hard to get that "perfect balance" between superb

usability and visual appearance. I must say that you've done

a excellent job with this. In addition,

the blog loads extremely quick for me on Internet explorer.

Outstanding Blog!

Also see my page>teachers.fju.edu.tw:16080When I originally commented I clicked the "Notify me when new comments are added" checkbox and now each time a

ReplyDeletecomment is added I get several e-mails with the same comment.

Is there any way you can remove

people from that service? Thanks!

Here is my website:sjhani.comgreat put up, very informative. I wonder why the opposite experts

ReplyDeleteof this sector do not notice this.

You should proceed your writing. I am sure, you

have a huge readers'

base already!

My web-site...wiki.transparency-initiative.orgWoah! I'm really digging the template/theme of this site. It's simple, yet effective.

ReplyDeleteA

lot of times it's very hard to get that "perfect balance" between user friendliness and visual appeal. I must say that you've done a superb job with this.

Additionally,

the blog loads very fast for me on Chrome. Outstanding Blog!

My blog post;http://theculinaryqueenbee.blogspot.de/2010/06/spanish-rice.htmlGood day! Do you know if they make any plugins to assist with

ReplyDeleteSearch Engine Optimization? I'm trying to get my blog to rank for some targeted keywords but I'm not seeing very good

gains. If you know of any please share. Thank you!

Here is my web blog:http://www.gftomlinson.co.uk/index.php/member/3097/I've been surfing online more than three hours today, yet I never found any interesting article

ReplyDeletelike yours. It’s pretty worth enough for me. In my opinion, if all web owners and bloggers made good content as you did, the web will be much more useful than ever before.

Look into my web page:5 day weather forecast murciaI precisely desired to thank you so much again. I do not know the things that I

ReplyDeletecould possibly have achieved without those pointers shown by you about

my industry. It had become an absolute troublesome

crisis in my view, nevertheless understanding the very skilled approach you

handled that

made me to jump with gladness. Now i'm grateful for

the help and then hope

you know what a powerful job you are always getting into instructing others using a web site. Most

likely you have never got to know any of us.

Also visit my web page:http://kiaspain.blogspot.co.ukHowdy! I simply want to give a huge thumbs up for the good info

ReplyDeleteyou may have right here on this post. I will likely be coming again to your blog for more soon.

Look at my web blog:http://findingblissinbooks.blogspot.ru/2012/10/review-blind-spot-by-laura-ellen.htmlYou are a very bright individual!

ReplyDeleteTake a look at my homepagehttp://casanaranjablog.blogspot.co.uk/2007/10/spain-uncensored.htmlVery good written post. It will be beneficial to everyone

ReplyDeletewho usess it, including yours truly :).

Keep up the good work - looking forward to more posts.

My website::http://microfinance.ca/I have read several good stuff here. Definitely worth

ReplyDeletebookmarking for revisiting. I

wonder how much effort you put to create such a great

informative web site.

Take a look at my webpage:puzzlepirates.ugu.plI savor, result

ReplyDeletein I found just what I used to be taking a look for.

You have ended my 4 day lengthy hunt! God Bless you man.

Have a nice day. Bye

Feel free to surf my web pagehttp://new.ain.az/Pretty element of content. I just stumbled

ReplyDeleteupon your web site and in accession capital to say that

I get actually enjoyed account your weblog posts.

Anyway I’ll be subscribing to your augment and even I success

you get

right of entry to persistently rapidly.

Here is my blog post;paddlingiowa.comVery nice info and right to the point. I don't know if this is

ReplyDeleteactually the best place to ask but do you guys have any ideea where

to hire some professional writers? Thank you :)

Here is my weblog::http://www.partnerschaftskomitee-muensingen.de/index.php?option=com_easygb&Itemid=39fantastic post, very informative. I wonder why the other experts of

ReplyDeletethis sector don't notice this. You must continue your writing. I am confident,

you've a huge readers' base already!

Also visit my web site::break-through.orgHi there! Would you mind if I share your blog with my myspace group?

ReplyDeleteThere's a lot of folks that I think would really enjoy your content.

Please let me know. Thanks

Also visit my web-site-ebenezerlepage.blogspot.ruHello there, I found your web site via Google

ReplyDeleteat the same time as searching for a related matter, your website got here up, it looks good.

I've bookmarked it in my google bookmarks.

Also visit my blog;http://www.singlefling.com/Hey there! Do you know if they make any plugins to assist with

ReplyDeleteSearch Engine Optimization? I'm trying to get my blog to rank for some targeted keywords but I'm not seeing very good

gains. If you know of any please share. Kudos!

my web page-http://collaborationwiki.lprgroup.com/index.php?title=User:DelgxmwpyYFantastic beat ! I wish to apprentice while you amend your

ReplyDeleteweb site, how can i subscribe for a blog website?

The account aided me a

acceptable deal. I had been a little bit acquainted

of this your broadcast offered bright clear

idea

My page:essentialweb.asiacertainly like your web site but you need to check the

ReplyDeletespelling on several of your posts. Several of them are rife with spelling problems

and I find it very bothersome to tell the truth nevertheless

I will definitely come

back again.

Also see my webpage>http://community.whyweteach.orgIt’s really a cool and helpful piece of info.

ReplyDeleteI’m glad that you shared this helpful info with us.

Please stay

us informed like this. Thank you for sharing.

my page::http://www.reeze.blogspot.co.uk/2008/05/new-kind-of-breast-cancerplease-read.htmlOnce I initially commented I clicked the -Notify me when new feedback

ReplyDeleteare added-

checkbox and now each time a comment is added I get 4 emails with the identical comment.

Is there any approach you possibly can take away me

from that service? Thanks!

My web page:www.salsamovements.comWhen I originally commented I clicked the "Notify me when new comments are added" checkbox and now each

ReplyDeletetime a

comment is added I get several emails with the same comment.

Is there any way you can remove me from that service?

Cheers!

Also visit my webpage...jlunjew.blogspot.frNice read, I just passed this onto a colleague who was doing some research

ReplyDeleteon that. And he

just bought me lunch because I found it for him smile Therefore let me rephrase that:

Thanks for lunch!

My web-sitel-ump.netI was suggested this website by my cousin. I'm not sure whether this post is written

ReplyDeleteby him as no one else know such detailed about my difficulty. You are

wonderful! Thanks!

Check out my web-site:studentkaren.seThanks for the good writeup. It actually was a entertainment

ReplyDeleteaccount it. Look complex to

far introduced agreeable from you! By the way, how can we communicate?

Here is my weblog-http://www.pk2diescape.smffy.com/index.php?action=profile&u=948Does your website have a contact page? I'm having a tough time locating it but, I'd like to

ReplyDeletesend you an e-mail. I've got some recommendations for your blog you

might be interested in hearing. Either way, great site and I look forward to seeing it improve over time.

Have a look at my homepage; http://blog-publico.blogspot.fr/

Here is my homepageBritish expatsAppreciating the persistence you put into your

ReplyDeleteblog and detailed information you provide. It's nice to come

across a blog every once in a while that isn't the same out

of date rehashed material. Fantastic read! I've bookmarked your site and I'm including your

RSS feeds to my Google account.

My site ... topseobacklinks.com

Also see my page>Costa Blanca Spain climateThis is very fascinating, You are an excessively professional blogger.

ReplyDeleteI have joined your feed and stay up for in quest of more of your

wonderful post. Additionally, I have shared your website in

my social networks!

My site - cgtrtve.org

Feel free to visit my blog post:homes for purchase in DoloresI am really loving the theme/design of your web site.

ReplyDeleteDo you ever run into any

browser compatibility problems? A handful of my blog visitors have complained about my website not operating correctly

in Explorer but looks great in Chrome. Do you have any ideas to help fix this

problem?

Here is my weblog ... http://justjulieb30.blogspot.ru/2012/08/googly-ghouls-for-challenge.html

Also see my website:TrackThank you for any other informative website. The

ReplyDeleteplace else may just I am getting that kind of information written in such an ideal way?

I've a project that

I'm just now operating on, and I've been at the look out for

such info.

my page: http://mythinks.in/

Also see my web page:houses for sale AlboxIt’s hard to find knowledgeable

ReplyDeleteindividuals on this matter, however you sound like

you understand what you’re speaking about! Thanks

Feel free to surf to my web page :: http://look-at-that.com/story.php?id=192044

Here is my web blog:spain weather forecast averageIt is really a nice and useful piece of info.

ReplyDeleteI am glad that you shared this

useful information with us. Please keep us up to date like this.

Thank you for

sharing.

My web-site www.nettyherawati.info

my website>spain new york VeraAppreciating the time and effort you put into your

ReplyDeletesite and in depth information you provide. It's good to come

across a blog every once in a while that isn't the same

unwanted rehashed material. Excellent read! I've saved your site and I'm including your

RSS feeds to my Google account.

Look at my web site; research.nodong.org

Have a look at my page;african brown knife fishMy programmer is trying to convince me to move to

ReplyDelete.net from PHP. I have always disliked the

idea because of the expenses. But he's tryiong none the less. I've been using

Movable-type on a variety of websites for about a year and am anxious about

switching to another platform. I have heard

great things about blogengine.net. Is

there a way I can import all my wordpress content

into it? Any help would be really appreciated!

Also visit my web blog ... www.blackseedproducts.com

Here is my blogproperties in DoloresAs I web-site possessor I believe the content matter here is rattling wonderful , appreciate it

ReplyDeletefor your hard work. You should keep it up forever! Good Luck.

Here is my web page - http://xxl-bookmarks.de

Here is my web site...clickbank search scriptIt is best to take part in a contest for one

ReplyDeleteof the best blogs on the web. I will

suggest this website!

My web-site :: teachers.fju.edu.tw:16080

Look into my web blog:sports in spain news La PalmaHey very cool blog!! Man .. Beautiful .. Amazing .

ReplyDelete. I will bookmark your

web site and take the feeds also…I'm happy to find so many useful

info here in the post, we need develop more strategies in this regard, thanks for

sharing. . . . . .

my webpage - gallosblancos.blogspot.com

My website;British expat CulleraHello, i read your blog from time to time and i own a similar one and i was just

ReplyDeletecurious if you get a lot of spam feedback? If so how do you

protect against it, any plugin or anything you can advise?

I get so much lately it's driving me

insane so any assistance is very much appreciated.

my page http://presleyfam.blogspot.fr

Feel free to surf my web-site:weather spain by monthYou made some clear points there. I looked on the internet for the

ReplyDeletesubject matter and found most people will consent

with

your site.

Here is my page;www.inrad.hcnet.usp.brHeya! I just wanted to ask if you ever have

ReplyDeleteany problems with hackers?

My last blog (wordpress) was hacked and I ended up losing many months of hard work due

to no data backup. Do you have any solutions to stop hackers?

Also visit my web-site::www.seocome.comI used to be very happy to seek out this web-site.I

ReplyDeletewanted to thanks to your time for this wonderful read!

! I positively having fun with every

little bit of it and I've you bookmarked to check out new stuff you

weblog post.

Stop by my web blog-http://www.registerthemes.com/2013/01/payment-receive-from-elegantthemes.htmlWonderful website. A lot of helpful information here.

ReplyDeleteI'm sending it to some buddies ans additionally sharing in delicious. And naturally, thank you in your effort!

Also visit my web page GFI Norte

I know this if off topic but I'm looking into starting my own blog and was curious what all is

ReplyDeleteneeded to get setup? I'm assuming having a blog like

yours would cost a pretty penny? I'm not very

web savvy so I'm not 100% sure. Any suggestions or advice

would be greatly appreciated. Many thanks

Also see my page:fdfda2.blogspot.co.ukValuable info. Fortunate me I found your web site

ReplyDeleteunintentionally, and I am shocked why this accident did not took place in advance!

I bookmarked it.

Have a look at my page:Www.Brosamer.usIncredible! This blog looks just like my old one! It's on a entirely

ReplyDeletedifferent subject but it has pretty much the same layout and design. Excellent choice of colors!

Here is my page;http://miningnamibia.blogspot.com/It's the best time to make a few plans for the future

ReplyDeleteand it's time to be happy. I have read this put up and if

I

could I desire to recommend you some fascinating things or advice.

Perhaps you can write next articles

relating to this article. I wish to read more

issues about it!

Look into my website;Notevayasestupida.blogspot.frThanks for one's marvelous posting! I truly enjoyed reading it, you will be a great author.I will be sure to bookmark your blog and will come back in the future. I want to encourage you to ultimately continue your great writing, have a nice holiday weekend!

ReplyDeleteFeel free to visit my blog post-wiki.stefankumli.chYou completed some nice points there. I did a search on the

ReplyDeletesubject and found a good number of

persons will consent with your blog.

Also visit my siteletsplej.plYou made certain fine points there. I did a search on the

ReplyDeletesubject and found the majority of

people will have the same opinion with your blog.

My website::altervista.orgWonderful goods from you, man. I have understand your stuff previous to and

ReplyDeleteyou're just extremely fantastic. I actually like what

you have acquired here, certainly like what you are saying and the way in which you

say it. You make it enjoyable and you still take care of to keep it wise. I

can not wait to read far more from you. This is really a terrific website.

my website:blogspot.comI was just looking for this info for a while. After six hours

ReplyDeleteof

continuous Googleing, finally I got it in your website.

I wonder what's the lack of

Google strategy that do not rank this kind of informative sites in top of the list.

Usually the top web sites are full of garbage.

My web blog;www.flokib.atI’d have to test with you here. Which is not something I often do!

ReplyDeleteI enjoy studying a post that may make individuals think.

Also, thanks for

permitting me to comment!

Also visit my bloghttp://us.vclart.netI have been absent for a while, but now I remember why I used to love this

ReplyDeletewebsite.

Thank you, I will try and check back more often. How

frequently you update your website?

Look at my site;www.ctrbolivia.comI do agree with all the ideas you've presented in your post. They're

ReplyDeletereally

convincing and will certainly work. Still, the posts are too

short for

starters. Could you please extend them a little from next time?

Thanks for the post.

My page...http://www.eeudf.org/eeudf_si/mediawiki/index.php?title=La_Finca_Golf_Links_-_Costa_Blanca_Spain_SpainThere are certainly a

ReplyDeletevariety of details like that to take into consideration.

That may be a nice level to deliver up. I provide the

ideas above as

common inspiration however clearly there are questions just like the one you

carry up where an important thing

will be working in sincere good faith. I

don?t know if finest practices have emerged round issues like

that, but

I'm certain that your job is clearly recognized as a fair game. Each boys

and girls feel the influence of only a second’s

pleasure, for the rest of their lives.

Also visit my website::http://nerdywordythirty.blogspot.ruThere are certainly a

ReplyDeletevariety of details like that to take into consideration.

That may be a nice level to deliver up. I provide the

ideas above as

common inspiration however clearly there are questions just like the one you

carry up where an important thing

will be working in sincere good faith. I

don?t know if finest practices have emerged round issues like that, but

I'm certain that your job is clearly recognized as a fair game. Each boys

and girls feel the influence of only a second’s

pleasure, for the rest of their lives.

my site::http://nerdywordythirty.blogspot.ruAs I web site possessor I believe the content material here is rattling magnificent , appreciate it for your efforts.

ReplyDeleteYou should keep it up forever!

Best of luck.

my web site-waslinfo.orgWonderful work! This is the type of information that are supposed to be shared around the net.

ReplyDeleteDisgrace on the seek engines for now not positioning this publish higher!

Come on

over and talk over with my web site . Thanks

=)

Also see my webpage-http://wiki.couo.ru/I’ve learn some excellent stuff here. Certainly worth bookmarking for revisiting.

ReplyDeleteI wonder how so much attempt you set to make such a magnificent informative site.

My weblog:freedesktop.orggreat post, very informative. I wonder why the opposite specialists of this sector do

ReplyDeletenot notice this.

You should proceed your writing. I am confident, you have a huge readers'

base already!

Also visit my website:http://Siryl.Mireene.com/wiki/index.php?title=Barcelona_Couriers-_The_actual_Nou_Method_to_Deliver_ParcelsHey! I just wanted to ask if you ever have any problems with hackers?

ReplyDeleteMy last blog (wordpress) was hacked and I ended up losing months of hard work due

to no data backup. Do you have any solutions to stop hackers?

Review my website-ghyang.pixnet.netWhat’s Happening i'm new to this, I stumbled upon this I've discovered

ReplyDeleteIt

absolutely helpful and it has aided me out

loads. I am hoping to give a

contribution & help different customers like its

aided me. Great

job.

Review my web page;http://essentialweb.asia/search.php?search=http://aaronwk.blogspot.fr/2012/06/so-are-you-fluent-in-spanish.htmlF*ckin’ awesome things here. I am very glad to see your post.

ReplyDeleteThanks a lot

and i'm looking forward to contact you. Will you please drop me a e-mail?

My web blog::http://www.assasincreed.cba.pl/UseBB/profile.php?id=133I think this is among the most vital information for me.

ReplyDeleteAnd i'm glad

reading your article. But wanna remark on few general things, The site style is

perfect, the articles is really excellent : D. Good job, cheers

Take a look at my website-hamseoul.krYou actually make it seem so easy together with your

ReplyDeletepresentation but I in finding this matter to be

actually one thing

that I feel I'd never understand. It kind of feels too complex and extremely large for me. I am

looking ahead to your subsequent put up, I’ll attempt to get the hold of it!

My web page;createmycircle.comYou actually make it seem so easy together with your

ReplyDeletepresentation but I in finding this matter to be actually one thing

that I feel I'd never understand. It kind of feels too complex and extremely large for me. I am

looking ahead to your subsequent put up, I’ll attempt to get the hold of it!

My web site-createmycircle.comDoes your site have a contact page? I'm having trouble locating it but, I'd like

ReplyDeleteto

shoot you an e-mail. I've got some suggestions for your blog you

might be interested in hearing. Either way, great site and I look forward to seeing it improve over time.

Here is my webpage...authenticlinks.comAwesome blog! Is your theme custom made or did

ReplyDeleteyou download it from

somewhere? A theme like yours with a few simple tweeks would really make

my blog shine. Please let me know where you got your design.

Many thanks

My webpage-thongmongkol.pck1.go.thI used to be suggested this web site by means of my cousin.

ReplyDeleteI'm not certain whether or not this put up is

written by way of him as nobody else recognize

such special

approximately my difficulty. You are amazing! Thank you!

Look into my web pagemongolnews.usThanks a bunch for sharing this with all of us you really know

ReplyDeletewhat you are talking about!

Bookmarked. Please also visit my website =). We could have a link exchange agreement between us!

My blog;lyczek.art.plGood - I should certainly pronounce, impressed with your web site.

ReplyDeleteI had no trouble

navigating through all tabs as well as related information ended up being truly

easy to do

to access. I recently found what I hoped for before you know it at all.

Reasonably unusual. Is

likely to appreciate it for those who add forums or something,

website theme . a tones way for

your client to communicate. Excellent task..

Feel free to surf my weblogsample2.foxco.euWith every little thing which

ReplyDeleteseems to be building within this particular subject

matter, a significant percentage of perspectives tend to be

very refreshing. On the other hand, I appologize, but I do not give credence to your entire plan,

all be it exciting none the

less. It appears to everybody that your commentary

are generally not totally rationalized and in actuality

you are generally yourself not even

totally confident of the argument. In any case I did appreciate reading through it.

my web blog :: HTTP://Www.dailyroads.com/profile.php?ID=171712

Great work! This is the typе οf info that are meаnt

ReplyDeleteto bе shaгeԁ acгoss thе web.

Disgrace on the sеek engineѕ for no longer positioning this publish higher!

Ϲome on оver and consult with my website

. Thanks =)

Rеview my wеb blog; raspberry keytone fusion

advertising and ***********

ReplyDeletewith Adwords. Well I am including this RSS to my email and

could glance out

for a lot extra of your respective interesting content.

Ensure

that you update this once more soon..

My web page :: Www.Adfty.net

I am now not sure where you are getting your

ReplyDeleteinformation, but great topic. I must spend a while learning

more or figuring out more. Thanks for wonderful information I was searching for

this info for my mission.

Here is my blog :: robbreport-us.easytech.com.ar

i think this was one of the best sites which gives to the mark knowledge with understandable efforts

ReplyDeletelike ur id but diagram should be given for bettere explanation

ReplyDeleteya

ReplyDelete