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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 🇮🇳

The Revolt of 1857: The Broader Manifestation of Emerging Mass Nationalism in India 🇮🇳सिंहासन हिल उठे राजवंशों ने भृकुटी तानी थी,
बूढ़े भारत में आई फिर से नयी जवानी थी,
गुमी हुई आज़ादी की कीमत सबने पहचानी थी,
दूर फिरंगी को करने की सबने मन में ठानी थी।
चमक उठी सन सत्तावन में, वह तलवार पुरानी थी,
बुंदेले हरबोलों के मुँह हमने सुनी कहानी थी,
खूब लड़ी मर्दानी वह तो झाँसी वाली रानी थी।। - सुभद्रा कुमारी चौहान (भारतीय कवि)
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…

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 किसी राष्ट्र या देश को आदर्श राष्ट्र या देश बनाने के लिए निःसंदेह एक आदर्श कानून व्यवस्था की आवश्यकता होती है, जिसके नजर में उस देश में रहने वाला सूक्ष्म जीव से लेकर विशालकाय जीव तक सभी एक समान होते है। किसी देश का स्वामी एक मनुष्य हो सकता है, इस पृथ्वी का स्वामी भी एक मनुष्य हो सकता है, किन्तु क्या इस सम्पूर्ण ब्रह्माण्ड का स्वामी भी एक मनुष्य हो सकता है, शायद नहीं .... अब यहां पर एक प्रश्न है उठता है, कि क्या इस सम्पूर्ण ब्रह्माण्ड को भी किसी स्वामी की आवश्यकता है? यदि किसी देश को स्वामी कि आवश्यकता है, यदि पृथ्वी को किसी स्वामी की आवश्यकता है, तो यकीनन इस ब्रह्मांड को भी एक स्वामी कि आवश्यकता है। इस ब्रह्मांड का स्वामी जो कोई भी है, उसके लिए ये पूरा ब्रह्मांड एक देश जैसा है, जिसके भीतर हमारे जैसे असंख्य जीव रह रहे है, इस ब्रह्मांड में हम अकेले नहीं है। यदि ये पूरा ब्रह्मांड एक देश है, तो निश्चित ही इस देश का भी एक नियम होगा कोई कानून होगा। यदि हम किसी देश की बात करें तो वहां कानून व्यवस्था बनाए रखने के लिए सैनिकों को तैनात किया जा…

Metamorphosing Sociopolitical Matrix of India under rule of East India Company

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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.)
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