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# Understanding Vector Group of Transformer (Part 1)

Home / Technical Articles / Understanding Vector Group of Transformer (Part 1)

## Introduction

Three phase transformer consists of three sets of primary windings, one for each phase, and three sets of secondary windings wound on the same iron core. Separate single-phase transformers can be used and externally interconnected to yield the same results as a 3-phase unit.

The primary windings are connected in one of several ways. The two most common configurations are the delta, in which the polarity end of one winding is connected to the non-polarity end of the next, and the star, in which all three non-polarities (or polarity) ends are connected together. The secondary windings are connected similarly. This means that a 3-phase transformer can have its primary and secondary windings connected the same (delta-delta or star-star), or differently (delta-star or star-delta).

It’s important to remember that the secondary voltage waveforms are in phase with the primary waveforms when the primary and secondary windings are connected the same way. This condition is called “no phase shift.”

But when the primary and secondary windings are connected differently, the secondary voltage waveforms will differ from the corresponding primary voltage waveforms by 30 electrical degrees. This is called a 30 degree phase shift. When two transformers are connected in parallel, their phase shifts must be identical; if not, a short circuit will occur when the transformers are energized.”

## Basic Idea of Winding

An ac voltage applied to a coil will induce a voltage in a second coil where the two are linked by a magnetic path. The phase relationship of the two voltages depends upon which ways round the coils are connected. The voltages will either be in-phase or displaced by 180 degree.

When 3 coils are used in a 3 phase transformer winding a number of options exist. The coil voltages can be in phase or displaced as above with the coils connected in star or delta and, in the case of a star winding, have the star point (neutral) brought out to an external terminal or not.

## Polarity

An AC voltage applied to a coil will induce a voltage in a second coil where the two are linked by a magnetic path.  The phase relationship of the two voltages depends upon which way round the coils are connected.  The voltages will either be in-phase or displaced by 180 deg.

When 3 coils are used in a 3 phase transformer winding a number of options exist. The coil voltages can be in phase or displaced as above with the coils connected in star or delta and, in the case of a star winding, have the star point (neutral) brought out to an external terminal or not.

When Pair of Coil of Transformer have same direction than voltage induced in both coil are in same direction from one end to other end. When two coil have opposite winding direction than Voltage induced in both coil are in opposite direction.

### Winding connection designations

• First Symbol: for High Voltage: Always capital letters.
•  D=Delta, S=Star, Z=Interconnected star, N=Neutral
• Second Symbol: for Low voltage: Always Small letters.
•  d=Delta, s=Star, z=Interconnected star, n=Neutral.
• Third Symbol: Phase displacement expressed as the clock hour number (1,6,11)

#### Example – Dyn11

Transformer has a delta connected primary winding (D) a star connected secondary (y) with the star point brought out (n) and a phase shift of 30 deg leading (11).

The point of confusion is occurring in notation in a step-up transformer. As the IEC60076-1 standard has stated, the notation is HV-LV in sequence. For example, a step-up transformer with a delta-connected primary, and star-connected secondary, is not written as ‘dY11’, but ‘Yd11’. The 11 indicates the LV winding leads the HV by 30 degrees.

Transformers built to ANSI standards usually do not have the vector group shown on their nameplate and instead a vector diagram is given to show the relationship between the primary and other windings.

## Vector Group of Transformer

The three phase transformer windings can be connected several ways. Based on the windings’ connection, the vector group of the transformer is determined.

The transformer vector group is indicated on the Name Plate of transformer by the manufacturer. The vector group indicates the phase difference between the primary and secondary sides, introduced due to that particular configuration of transformer windings connection.

The Determination of vector group of transformers is very important before connecting two or more transformers in parallel. If two transformers of different vector groups are connected in parallel then phase difference exist between the secondary of the transformers and large circulating current flows between the two transformers which is very detrimental.

## Phase Displacement between HV and LV Windings

The vector for the high voltage winding is taken as the reference vector. Displacement of the vectors of other windings from the reference vector, with anticlockwise rotation, is represented by the use of clock hour figure.

IS: 2026 (Part 1V)-1977 gives 26 sets of connections star-star, star-delta, and star zigzag, delta-delta, delta star, delta-zigzag, zigzag star, zigzag-delta. Displacement of the low voltage winding vector varies from zero to -330° in steps of -30°, depending on the method of connections.

Hardly any power system adopts such a large variety of connections. Some of the commonly used connections with phase displacement of 0, -300, -180″ and -330° (clock-hour setting 0, 1, 6 and 11).

Symbol for the high voltage winding comes first, followed by the symbols of windings in diminishing sequence of voltage. For example a 220/66/11 kV Transformer connected star, star and delta and vectors of 66 and 11 kV windings having phase displacement of 0° and -330° with the reference (220 kV) vector will be represented As Yy0 – Yd11.

The digits (0, 1, 11 etc) relate to the phase displacement between the HV and LV windings using a clock face notation. The phasor representing the HV winding is taken as reference and set at 12 o’clock. Phase rotation is always anti-clockwise. (International adopted).

Use the hour indicator as the indicating phase displacement angle. Because there are 12 hours on a clock, and a circle consists out of 360°, each hour represents 30°.Thus 1 = 30°, 2 = 60°, 3 = 90°, 6 = 180° and 12 = 0° or 360°.

The minute hand is set on 12 o’clock and replaces the line to neutral voltage (sometimes imaginary) of the HV winding. This position is always the reference point.

#### Example

• Digit 0 =0° that the LV phasor is in phase with the HV phasor
Digit 1 =30° lagging (LV lags HV with 30°) because rotation is anti-clockwise.
• Digit 11 = 330° lagging or 30° leading (LV leads HV with 30°)
• Digit 5 = 150° lagging (LV lags HV with 150°)
• Digit 6 = 180° lagging (LV lags HV with 180°)

When transformers are operated in parallel it is important that any phase shift is the same through each. Paralleling typically occurs when transformers are located at one site and connected to a common bus bar (banked) or located at different sites with the secondary terminals connected via distribution or transmission circuits consisting of cables and overhead lines.

 Phase Shift (Deg) Connection 0 Yy0 Dd0 Dz0 30 lag Yd1 Dy1 Yz1 60 lag Dd2 Dz2 120 lag Dd4 Dz4 150 lag Yd5 Dy5 Yz5 180 lag Yy6 Dd6 Dz6 150 lead Yd7 Dy7 Yz7 120 lead Dd8 Dz8 60 lead Dd10 Dz10 30 lead Yd11 Dy11 Yz11

The phase-bushings on a three phase transformer are marked either  ABC, UVW or 123 (HV-side capital, LV-side small letters). Two winding, three phase transformers can be divided into four main categories

 Group O’clock TC Group I 0 o’clock, 0° delta/delta, star/star Group II 6 o’clock, 180° delta/delta, star/star Group III 1 o’clock, -30° star/delta, delta/star Group IV 11 o’clock, +30° star/delta, delta/star Minus indicates LV lagging HV, plus indicates LV leading HV

To be continued…

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### Jignesh Parmar

Jignesh Parmar has completed M.Tech (Power System Control), B.E (Electrical). He is member of Institution of Engineers (MIE), India. He has more than 13 years experience in transmission & distribution-energy theft detection and maintenance electrical projects.

### 92 Comments

1. Hamed
Dec 03, 2020

Hello,

Is is possible to connect only two transformers with two different vector group to each other?

There would be no other transformers on the grid. Only to transformer connected to eachother but different vector groups…

Thank you

2. Joni Barua
Sep 21, 2020

Sir,
If generator transformer vector group is Dyn1 and Distribution Transformer vector group is also Dyn1 i.e. phase displacement exist between generator and load voltage. Is there any problem in power flow if transformer paralleling is not required? What problems may arise from this phase displacement except transformer paralleling?

3. Rajasekhar Reddy Adala
Dec 02, 2019

Their is also a vector group YNd9, but not told about this.

4. Keyuri R Kariya
Nov 14, 2019

which vector group apply in 24 pulse furnace transformer

5. THAMBI GNANABALAN K
Oct 13, 2019

Dear sir,

#1 In Dy11 condition you have mention 330 deg lagging and 30 deg lead. How it is possible and when.?

#2 In practice Dy11 is connected to load which is mostly lagging power factor how the 30 deg lead is possible ?

• Engr. Mustafizur Rahman
Dec 21, 2019

Vector group has no relation with load power factor. Better you draw a clock marking with 1,2…upto12 and then highlight the point 11. Now if you count how far the Point 11 from 12. You will find that its 330 deg far but in clock wise direction and again only 30 deg far but this time in Anti clock wise direction. Thus 330 deg Lag = (360-330=) 30 deg Lead. Likewise 300 deg Lag= (360-300 =) 60 deg Lead and so on.

• Harihar Behera
Jun 12, 2020

why neutral point not available in induction furnace transformer. The vector group is dy11. Ratio of transformer is 6000 KVA 11/0.690-0.690 kv

6. JOSE PINEDA
Oct 09, 2019

Dear Sir.

I would like to know if someone know about the conection of Ynad .
Please let me know to my email [email protected]

Many thanks.

7. ENGR A A MAHMUD
Aug 23, 2019

Recently in one project we have found that system design as below

Source Power supply by 4nos. 1.5MW Generator ( output 415V, 50Hz) and generator are in star connection, for that use 4nos. step up transformer they use vector group YNd1 ( 415V / 11KV) and after 400M distance where they need power do Step down by 4nos. Transformer use vector group Dyn11 ( 11KV / 415V )

We ask them why they design like this, they informed us that at the time of step up it will be in lagging and at the time of step down it will be leading, so their will be no phase angel. it will work perfectly

Can any one guide us or clarify us more ?

Thanking you in advance for kind support

Best Regards

Mahmud

• Shaukat Amin
Aug 30, 2019

How you protect the earth fault at 11 KV cable.you should use any one side star Y connection for earth.if your 11KV cable ground then append. because you use delta connection on both side of 11 KV.

• Lalremruatkima Khawlhring
Mar 29, 2020

YNd1 is 30°lagging while Dyn11 is 330°lagging (which is similar to 30°leading according to the lecture above). So the resultant angle will be in phase…

8. RatnaKumar
Aug 09, 2019

Nice information…

9. Madan Lal Sachdeva
Aug 08, 2019

Delta connection is provided on the generator side to avoid flow of 3rd harmonics on generator side. The other side may be Star or delta. The star side provides facility for detection of earth fault and operate ground fault protection.In case of delta connection, for ground fault detection ,Zig-zag transformer is required to be provided for creating artificial neutral for passage of current to earth.

In case of delta connection , each phase winding full insulation over the complete length of coil where as in case of Star connection for system above 66kV, the insulation on neutral side is reduced ans cost of transformer is reduced.
As regards selection of vector connection. the delta connection is always connected to generator side and other side connection is why for ground fault detection otherwise, additional Zig -Zag transformer is to be provided with delta connection for ground fault detection.
On load side, the phase angle of the existing bus is to be ascertained and then select the vector arrangement of new transformer. Under unavoidable circumstances, phase shifting transformer would be required to be provided to avoid unbalance voltages.
Neutral connection of star connected winding shall not be left unconnected/ floating from earth as this will cause unbalance phase voltages, avoid detection of ground fault current and may adversely effect the safety of operator/ public.

10. Tansukh
Feb 26, 2019

Dear Sir,

we are doing one power project in abrod middle east and capacity of 4Mwe*4. we choose the each generator 1250kva, 415v to 3.3kv transformer. we interest to avoid NGR. Please suggest transformer

11. Tansukh
Feb 26, 2019

Dear Sir,

We are going on one gas base power project of 6 MWe. power generation is LT 415V with synch. After step up 415 to 11KV. we plan to installation 5 transformer to each generator. we choose transformer capacity of 2000kva*2 and 1600*3. Please suggest vector group. we are not interest to use NGR.

12. Tony Hazouri
Jan 24, 2019

Dear Sir’s

I need to synchronize a steam turbine 6.3 KV With the bus 11 KV
I need to request transformer step up 6.3 KV TO 11 KV
So what is the connection of the transformer should be Dd0 or Yy0 i don’t want any phase shifting.

any idea ?

Thank you

13. Naren
Jan 21, 2019

First of all Thanks for your Article on Vector Groups. All the Points are clear to understand. I’m little bit confused with Dy5 and Dy7 vector group diagrams. Can you please explain that alone for me.

• Ken T
Jul 28, 2019

Have a look at the Delta side, It’s different. The Star side is the same.

14. hasibul ahsan
Sep 11, 2018

I have a question about the transformer polarity. How does clockwise and anticlockwise winding changes the polarity of the secondary winding? According to the Lenzt law the polarity of the secondary winding should not be as such as to oppose the change in flux in primary?
Should not be the polarity always same? either positive or negetive?

I am creating a page about the transformers principle here
http://www.hasibulahsan.epizy.com

15. Srijan Gangopadhyay
Aug 11, 2018

What is principal purpose/necessity of vector grouping for 3 phase transformer ?
Because I didn’t think only for the parallel operation is the main reason behind it but I can’t conclude it properly, so please help me to understand this matter…..

16. Md. Farhaduzzaman
Apr 05, 2018

Thanks to the writer for his wonderful article.

17. Sugandh
Mar 14, 2018

How can I tell “Yd11″(which you have mentioned as a step-up) is not a step down transformer.Please explain

18. Dhimant Gondaliya
Mar 13, 2018

sir how can i connect the auto transformer at phase shifting of 40 degree for -20 and +20 degree for deferential delta connection

19. a Hamd
Feb 27, 2018

I am reading an AUTO transformer Name plate and it says;;;; YNa0d11

Can someone explain what does letter a and digit 0 stand for.

Thanks

• Santhosh Ramayanam
Mar 12, 2018

“a” stands for auto-transformer.

20. M. Husnain
Jan 16, 2018

Why Vector group Yd3, Dy3 are omitted however they are possible connections?

21. S Srinivasan
Jan 03, 2018

Sir. Why all the distribution transformers in India is generally Dyn11? Any specific reason for that? Why can’t other vector groups not preferred?

22. Anand K V
Nov 18, 2017

Hello Sir,
How shall we mention Vector Group for a 3-Phase LT Transformer 415V/30V with Open Delta configuration for both Primary & Secondary Sides. Phase shift shall be 0 Deg.

23. Jerry Kwabla Agbo
Aug 24, 2017

Am very happy and enjoy your thesis and details.
I work with power company ,please I will like to know how load balancing.On 500kva transformer if Red phase is 400A ,Yellow phase is 345A and Blue phase is 258A lastly Natural current is 211A. Please what do I do on such load balancing.I would be glad if I will get some magazine’s and small tools (instruments) to assist me on my work.
Thanks for your blessing.

My address is ECG Accra west , P.O.Box 6348.North Accra,West African Ghana.

• Deepak Kumar Mongia
May 29, 2018

Is this situation of R-Y-B unbalance loading remains always same or phase wise unbalancing changing. Means more load is sometime on R phase , sometimes on Y phase and so on . If unbalancing pattern is always same phase wise then it will be easy to balance by withdrawing single phase load from R and putting it on B phase.
But if unbalancing is randomly on different phases then segregate 3 phase and 1 phase load; identify the load causing unbalancing and try to divide the single phase load equally on three phases for this you need to modify your distribution on different electrical panels and may be some wiring changes are also required for distributing the load.

24. Darren
Jul 28, 2017

Really appreciated this article helped me greatly. Explained clearly. looking forward to getting more transformer theory explained

25. Saadat Ullah
Mar 03, 2017

Can i connect Dyn11yn11 parallel with Dy11y11 – DeltaHV side Dual LV winding star connected? I have 7 dry transformers with Dyn11yn11 configration but we didn’t connect neutral with the transformer. Now i am thinking to order a new oil transformer of Dy11y11 configuration. According to my understanding, there won’t be any problem because the difference is just having neutral connection out or not?

• Khan
Jan 04, 2018

When you want to go for parallel you have to check follows.

1)both transformer’s same vector group.
2)impedance volts % variation should be within 0.5 %of both transformer’s.
3) ‘0’ voltage should be measured in same phase of one transformer to the second transformer.

Example:TR-1 secondary ‘r’ phase to TR-2 secondary ‘r’ phase voltage should be ‘0’. and repeat for all phases.

26. Jacqueline Mukangala
Nov 21, 2016

ATT: SALES

Kindly quote us for the following;

Transformer
Voltage: 11KV/3.3KV
Rating: 1250KVA
Vector Group: DYn11

Regards,
Jacqueline

PLAGGMAN INVESTMENTS LIMITED
Plot # 1280 Timo Building
Freetown Road, Second Class
Light Industrial Area
Kitwe, Zambia

Office: +260 212 221128
Mobile: +260 963 465173

27. kiko vargas
Sep 26, 2016

my colleague needed to fill out a form recently and located a web service that has a searchable forms database . If people are wanting it as well , here’s a https://goo.gl/5auDai

28. GOURAV
Aug 01, 2016

why we need phase shift at secondary side is it necessary if yes why?

29. B Raj Thakur
Jul 25, 2016

Thanks a lot sir

30. Md.Siddique Shariful Islam.
Apr 23, 2016

Thanks Sir,
We need more …..

31. ashok
Apr 18, 2016

on what vector group a transformer is selected for a particular application.

• Fabrice de Lapparent
Jun 21, 2016

I have a set up with one stepup transformer 1250 kVA 415 V/22 kV and then another step down transformer 600 m away 650 kVA 22 kV / 415 V. How should I choose the vector group for each transformer. The cos phi is >= .8. The application is for a resort hotel.
Thank you

32. K.V.RAO
Apr 11, 2016

Nice explanation on vector groups of transformers. Pl comment on doubts raised on the content as the explanation taken in right earnest by many engineers. Also pl explain the significance of 30 degree multiple. Thanks a lot to the author for helping many engineers in learning Electrical Engineering in a layman’s style. My best wishes for many more contributions

33. Mihai
Apr 05, 2016

Very good explanation, but one question rises: what’s the reason for all that variety of vector groups (I mean, why is it required to have that many phase shifts combinations, for what use)? Thanks.

• Saha
Feb 03, 2017

When we try connect different transformer in parallel

34. Abdelazeem
Feb 01, 2016

thanks a lot to your your discussion very good thanks a lot

35. raghubir singh khokher
Jan 07, 2016

How to confirm which vector group one three phase transformer belongs to, please explain calculations & connections made for
different vector groups for testing

36. Deepak
Nov 18, 2015

Can we have common grounding/earthing for neutral of two or more power transformers and DG sets (at industrial units). If not then why. Also can we have common earthing for neutral and body of transformer.

37. sajjad
Oct 28, 2015

dear sir, i want to know why it is so important to build vector group in a transformer, why we not use a transformer without any vector group

38. Rabiul
Sep 16, 2015

I will convert 360-380v to 415 v. What will be vector group for that. Both windings are Star.

• ompscruz
Jan 29, 2020

connect 2 -360 in series and have those be connected in delta, then the secondary should be connected in star and it will give you a 415 volts

39. Aqeel
Sep 02, 2015

If you say the rotation anti-clock then TR. Dyn11 LV lags HV by 30 degree and Dyn1 LV leads HV by 30 degree . I think clock – wise is correct

• jay
Nov 22, 2017

Generally direction is taken as anticlockwise.

40. phaneendra kumar
Aug 02, 2015

Why the transformers are not designed at Higher impedance (>20%) even though current density suits the short circuit temperature(Asper IEC—180 degrees )?Please clarify the doubt ?

• Shayaque Safi
Feb 16, 2017

As far as you increase the impedance, short circuit current reduces but at the same time efficiency decreases.

41. Bob Robinson
Jul 09, 2015

My question is ‘why did we need different types in the first place?’

42. Francisco Gomez
Jun 03, 2015

Thanks for your explanation about vector group. I would like that you verify this affirmation. If i have a transformer Dy11 step down (33/0.415kV) connected in series with a transformer Dy11 step up (11/0.415kV), we are going to have 0 degrees of difference between 33kV and 11kV sides.
Thanks

43. mojtaba
Jun 01, 2015

thank you very much for your preamble

44. mustafa
May 21, 2015

Hi
I was working in a project and I have seen that there are two different power transformers has been connect in parallel even they were have different primary and secondary connection.
one was Dy11 and the other was Yd5.
any one can explain how this performed.

45. Chet Ram Yadav
May 16, 2015

Dear Sir,

I have faceting problem in testing of Transformer Vector Group DY11Y11Y11Y11,(380VX4/33000V for solar Plant) I have ask to client for factory test report but he is not providing me.

You are requested please help me, I am electrical engineer and working for solar power plant first time.

46. vijay
Apr 22, 2015

Hello sir,
I have design 480kva trx.Dry type.On primary side Delta connection & on secondary side Star connection.
& both have 2 layers of winding.
I want vector group Dy1 then what is connection (both delta & star)plz guide me.my email [email protected] you

47. s.balasubramanian
Mar 23, 2015

Vector diagram is least understood by many. Most important is how you draw vector diagram when trafo are connected in any manner and how to draw conclusion on phase shift. can u develop some OR if it is OK I can try my hand at it

48. YOGESH SHARMA
Mar 08, 2015

Sir
what in the mean of Lio vector group and why we can you the other vector group in place of this vector group.

49. bharat baravaliya
Feb 23, 2015

sir, we have to need ans of diff between vector group of dy1 and dy11 and als0 dy1 is used instead of dy11?

50. Ananda kumar J
Feb 16, 2015

your explanation is very good

51. Elumalai Ramasamy
Feb 06, 2015

Dear Sir We need Phase Shifting Transformer Design details

52. jonathan
Jan 20, 2015

very good explanation and great mind

53. Ezeh Doris Oluchi
Jan 09, 2015

From the Vector group YznII of a particular transformer, how would you know that the Ratio test on the HV side of a transformer has failed? ie from which range(the input to the output should be before you can say it has failed )

54. shail
Jan 06, 2015

what is the use of vector group (phase displacement) in distribution transformer. can i use that transformer which have no phase displacement in voltage b/w praimary and secendry w/d.

55. NANJAPPA
Nov 29, 2014

it is a good collection and enjoy reading and for working practical experience in international market.

56. Muralikrishnan
Nov 03, 2014

3ph ac magnetic mutual indexon vector groups and clock position super

57. shivani
Oct 21, 2014

This info is realy useful because the connections of vector groups r confusing me very much but now i understand

58. Heri
Sep 26, 2014

What i need if will install synchronizer generator to bus if VT sensing at before and after transformer ?. The transformer vector is Yd11.

59. imamhussain
Sep 02, 2014

thanks for giveing above electricle information for vecter group

60. Chris
Aug 21, 2014

Very useful, but often these articles remind me of my university days where the real world application of the information is missed.

Can you please explain why and when you would use these different vector groups on a transformer?

Thanks

61. Rohan Thurstans
Aug 01, 2014

Mostly a good article except Winding Connection Designation for star is Y not S. But more importantly most of the clock notation vector diagrams are wrong. Please fix these I have had two people this week give me wrong vector diagrams because they copied your errors.

• Gobinda
Sep 12, 2014

Kindly tell which diagrams are wrong & explain.

62. devadath g
Jul 29, 2014

How to find out Different vector group ?

63. masood
Jul 17, 2014

Thank you. when it will be continued?

64. aziz
Jun 04, 2014

whats the difference between Dyn11 and Dyn5 in 3-phase transformers, which connection better.
thx

65. Cookiess
May 14, 2014

Why it does not have Yy4 (120 lagging) ?

High voltage winding; use Y0
and Low voltage winding; use Y8

after i read your article. i think my above connection we can get Yy4 (120 lagging)

Please advise.

66. feras mahfoud
May 14, 2014

thanks a lot for that article.

67. al amin osman omer
May 14, 2014

very nice

68. Srikant
Apr 17, 2014

Why do dd and yy winding cannot have 30 or 60 degree phase shift in vector group formation.

69. Beny pardede
Apr 16, 2014

Very nice article
but I think your Additive and Substractive diagram is not right.
:)

70. Radhakrishnan K A
Dec 10, 2013

Dear Jignesh

This is an article well explained in common mans language.I have been an avid reader of many an article published by you and every article is just great.Thanks for sharing all this.

Radhakrishnan K A

71. mdburanou
Nov 06, 2013

Please check the additive polarity symbolic daigram

72. vasanthu
Oct 22, 2013

I have a Delta/Star Step down transformer with a vector group Dyn11 written on the name plate. From the article here I understood that secondary side winding is phase shift by 30 degrees with respect to primary side winding. They also say that this configuration eliminates third harmonics in the system. I don’t clearly understand how it is helping to eliminate the third harmonics. I would appreciate if some one could give a better explanation on this with graph or equations if possible. Thanks a lot..

73. rkkatrix
Jul 25, 2013

simple and excellent … great work jignesh !!!!

74. khuram388
Feb 20, 2013

realy great effort sir

75. yogesh parmar
Nov 20, 2012

dear jignesh sir

your are really a great contributor in EEP.your all articles are mindblowiing.
thanking you
from yogesh parmar

76. saad1966
Aug 07, 2012

really it is wonderful effort…..thanks so much

77. rachidakoum
Jun 05, 2012

really it is wonderful effort.
thanx

78. Edvard
Jun 03, 2012

This is the far best explanation of vector group meaning and usage! Thank you very much Jignesh!

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