### Three Dimensional Geometry (part - 2) , The Planes | study material for IIT JEE | concept booster, chapter highlights/

THREE DIMENSIONAL GEOMETRY (PART - 2), THE PLANES

THE PLANESPlane is the surface such that if any two points are taken on it, then the line joining the two points lies on it.
General equation of plane is given as -  ax + by + cz + d = 0 , where a ,b and c is not equal to zero.
POINTS TO BE REMEMBERED 1). a, b and c are the directions ratios of the normal to the plane ax + by + cz + d = 0.

2). Equation of the yz - plane is x = 0

3). Equation of the zx - plane is y = 0

4). Equation of the xy - plane is z = 0

5). Equation of the any plane parallel to the xy - plane is z = c. Similarly for Planes parallel to yz and zx is x = c and y = c
EQUATION OF THE PLANE IN NORMAL FORMVECTOR FORMIf n̂ be a unit vector normal to a given plane and d be the length of the perpendicular from the origin to the plane, then the equation of the plane is given by -                           r.n̂ = d CARTESIAN FORMIf l, m, n are the directions cosines of the normal to the plane and d is the perpendicular distan…

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### The Revolt of 1857: The Broader Manifestation of Emerging Mass Nationalism in India ๐ฎ๐ณ

The Revolt of 1857: The Broader Manifestation of Emerging Mass Nationalism in India ๐ฎ๐ณเคธिंเคนाเคธเคจ เคนिเคฒ เคเค े เคฐाเคเคตंเคถों เคจे เคญृเคुเคी เคคाเคจी เคฅी,
เคฌूเคข़े เคญाเคฐเคค เคฎें เคเค เคซिเคฐ เคธे เคจเคฏी เคเคตाเคจी เคฅी,
เคुเคฎी เคนुเค เคเค़ाเคฆी เคी เคीเคฎเคค เคธเคฌเคจे เคชเคนเคाเคจी เคฅी,
เคฆूเคฐ เคซिเคฐंเคी เคो เคเคฐเคจे เคी เคธเคฌเคจे เคฎเคจ เคฎें เค ाเคจी เคฅी।
เคเคฎเค เคเค ी เคธเคจ เคธเคค्เคคाเคตเคจ เคฎें, เคตเคน เคคเคฒเคตाเคฐ เคชुเคฐाเคจी เคฅी,
เคฌुंเคฆेเคฒे เคนเคฐเคฌोเคฒों เคे เคฎुँเคน เคนเคฎเคจे เคธुเคจी เคเคนाเคจी เคฅी,
เคूเคฌ เคฒเคก़ी เคฎเคฐ्เคฆाเคจी เคตเคน เคคो เคाँเคธी เคตाเคฒी เคฐाเคจी เคฅी।। - เคธुเคญเคฆ्เคฐा เคुเคฎाเคฐी เคौเคนाเคจ (เคญाเคฐเคคीเคฏ เคเคตि)
Around 3000 rebellious Indian soldiers erupted with excessive outrage on 10 May 1857 against the oppressive colonial system in the garrison town of Merrut. Crossing Jamuna river, the revolutionaries entered Delhi, attacked British cavalry posts, police stations, killed European officials and ascertained their control over Red Fort and Salimgarh Fort. The upsurging rebellion gained the political support of Nana Saheb- the adopted son of late Peshwa Baji Rao, the queen of Jhansi Rani Laxmibai, Mughal Emperor Bahadur Shah ZafarTantia Tope, Rani Awantibai. Identifying with the ong…

### Three Dimensional Geometry (part - 2) , The Planes | study material for IIT JEE | concept booster, chapter highlights/

THREE DIMENSIONAL GEOMETRY (PART - 2), THE PLANES

THE PLANESPlane is the surface such that if any two points are taken on it, then the line joining the two points lies on it.
General equation of plane is given as -  ax + by + cz + d = 0 , where a ,b and c is not equal to zero.
POINTS TO BE REMEMBERED 1). a, b and c are the directions ratios of the normal to the plane ax + by + cz + d = 0.

2). Equation of the yz - plane is x = 0

3). Equation of the zx - plane is y = 0

4). Equation of the xy - plane is z = 0

5). Equation of the any plane parallel to the xy - plane is z = c. Similarly for Planes parallel to yz and zx is x = c and y = c
EQUATION OF THE PLANE IN NORMAL FORMVECTOR FORMIf n̂ be a unit vector normal to a given plane and d be the length of the perpendicular from the origin to the plane, then the equation of the plane is given by -                           r.n̂ = d CARTESIAN FORMIf l, m, n are the directions cosines of the normal to the plane and d is the perpendicular distan…

### " THE LAWS OF NATURE" เคช्เคฐเคृเคคि เคे เคจिเคฏเคฎ, เคिเคธเคธे เคोเค เคญी เคฌเค เคจเคนीं เคธเคเคคा, เคเคช เคญी เคจเคนीं | เคช्เคฐเคृเคคि เคे เคคीเคจ เคुเคฃ เค्เคฏा เคนै?|

"เคฒॉเค เคเคซ เคจेเคเคฐ" เคเคนเคคा เคนै -

เคช्เคฐเคृเคคि เค्เคฏा เคนै?
เคिเคธी เคฐाเคท्เค्เคฐ เคฏा เคฆेเคถ เคो เคเคฆเคฐ्เคถ เคฐाเคท्เค्เคฐ เคฏा เคฆेเคถ เคฌเคจाเคจे เคे เคฒिเค เคจिःเคธंเคฆेเคน เคเค เคเคฆเคฐ्เคถ เคाเคจूเคจ เคต्เคฏเคตเคธ्เคฅा เคी เคเคตเคถ्เคฏเคเคคा เคนोเคคी เคนै, เคिเคธเคे เคจเคเคฐ เคฎें เคเคธ เคฆेเคถ เคฎें เคฐเคนเคจे เคตाเคฒा เคธूเค्เคท्เคฎ เคीเคต เคธे เคฒेเคเคฐ เคตिเคถाเคฒเคाเคฏ เคीเคต เคคเค เคธเคญी เคเค เคธเคฎाเคจ เคนोเคคे เคนै। เคिเคธी เคฆेเคถ เคा เคธ्เคตाเคฎी เคเค เคฎเคจुเคท्เคฏ เคนो เคธเคเคคा เคนै, เคเคธ เคชृเคฅ्เคตी เคा เคธ्เคตाเคฎी เคญी เคเค เคฎเคจुเคท्เคฏ เคนो เคธเคเคคा เคนै, เคिเคจ्เคคु เค्เคฏा เคเคธ เคธเคฎ्เคชूเคฐ्เคฃ เคฌ्เคฐเคน्เคฎाเคฃ्เคก เคा เคธ्เคตाเคฎी เคญी เคเค เคฎเคจुเคท्เคฏ เคนो เคธเคเคคा เคนै, เคถाเคฏเคฆ เคจเคนीं .... เคเคฌ เคฏเคนां เคชเคฐ เคเค เคช्เคฐเคถ्เคจ เคนै เคเค เคคा เคนै, เคि เค्เคฏा เคเคธ เคธเคฎ्เคชूเคฐ्เคฃ เคฌ्เคฐเคน्เคฎाเคฃ्เคก เคो เคญी เคिเคธी เคธ्เคตाเคฎी เคी เคเคตเคถ्เคฏเคเคคा เคนै? เคฏเคฆि เคिเคธी เคฆेเคถ เคो เคธ्เคตाเคฎी เคि เคเคตเคถ्เคฏเคเคคा เคนै, เคฏเคฆि เคชृเคฅ्เคตी เคो เคिเคธी เคธ्เคตाเคฎी เคी เคเคตเคถ्เคฏเคเคคा เคนै, เคคो เคฏเคीเคจเคจ เคเคธ เคฌ्เคฐเคน्เคฎांเคก เคो เคญी เคเค เคธ्เคตाเคฎी เคि เคเคตเคถ्เคฏเคเคคा เคนै। เคเคธ เคฌ्เคฐเคน्เคฎांเคก เคा เคธ्เคตाเคฎी เคो เคोเค เคญी เคนै, เคเคธเคे เคฒिเค เคฏे เคชूเคฐा เคฌ्เคฐเคน्เคฎांเคก เคเค เคฆेเคถ เคैเคธा เคนै, เคिเคธเคे เคญीเคคเคฐ เคนเคฎाเคฐे เคैเคธे เคเคธंเค्เคฏ เคीเคต เคฐเคน เคฐเคนे เคนै, เคเคธ เคฌ्เคฐเคน्เคฎांเคก เคฎें เคนเคฎ เคเคेเคฒे เคจเคนीं เคนै। เคฏเคฆि เคฏे เคชूเคฐा เคฌ्เคฐเคน्เคฎांเคก เคเค เคฆेเคถ เคนै, เคคो เคจिเคถ्เคिเคค เคนी เคเคธ เคฆेเคถ เคा เคญी เคเค เคจिเคฏเคฎ เคนोเคा เคोเค เคाเคจूเคจ เคนोเคा। เคฏเคฆि เคนเคฎ เคिเคธी เคฆेเคถ เคी เคฌाเคค เคเคฐें เคคो เคตเคนां เคाเคจूเคจ เคต्เคฏเคตเคธ्เคฅा เคฌเคจाเค เคฐเคเคจे เคे เคฒिเค เคธैเคจिเคों เคो เคคैเคจाเคค เคिเคฏा เคा…

### Metamorphosing Sociopolitical Matrix of India under rule of East India Company

Metamorphosing Sociopolitical Matrix of India under the Regime of East India Company till 1857

Under the colonial rule of the British Imperial Legislative Government and East India Company, the sociopolitical structure of India had undergone a massive change at several levels. East India Company was evolving as a crucial political strength in India by late eighteenth century after deposing prominent regional powers like Bengal, Bombay etc. The Company introduced repressive policies for expansion of territories as elaborated in the article Emergence of East India Company as an Imperialist Political Power in India.
Functioning as an administrative and political entity in India, EIC launched numerous political, social and education-related policies that considerably affected various sections of society like peasants, women, children, industrial sectors and handicrafters. The prime objective of this article is to shed light on the sociopolitical matrix of British India to understand the sta…

### Was East India Company supremely functioning as a Colonial Trading Group till 1857?

Was British East India Company supremely functioning as a Colonial Trading Group till 1857?

After acquiring the royal charter from the ruler of England in 1600, the British East India Company attained a monopoly on trade with East. The company eliminated competition in business; asserted control over Bengal after Battle of Plassey 1757; achieved Diwani rights ( i.e. revenue collection rights over Bengal, Bihar and Orisha) after Treaty of Allahabad 1765 and emerged as a supreme political power by the middle eighteenth century. But interestingly, the company experienced financial collapse by the second half of the eighteenth century because of nepotism and persistence of corruption in company officials. ( Such corrupt officials were often referred as nabobs- an anglicised form of the nawab.)
British Parliamentary Government investigated the inherent functioning of the company and introduced several acts to induce discipline in the company officials. Regulating Act/ Charter Act (1773):Thi…