#Vector Algebra Class 12 Solutions

[drmikewatts]

Soft Computing, Volume 29, Issue 6, March 2025

1) On subresiduated lattice ordered commutative monoids and some of its subvarieties

Author(s): Juan Manuel Cornejo, Hernán Javier San Martín, Valeria Anahí Sígal

Pages: 2517 - 2529

2) Dynamic updating approximations of local multigranulation neighborhood covering rough sets

Author(s): Qi Shi, Yan-Lan Zhang

Pages: 2531 - 2550

3) Relationships between various ideals in L-algebra

Author(s): S. Saidi Goraghani, R. A. Borzooei

Pages: 2551 - 2562

4) Numerical algorithm for solving third-order Emden–Fowler type pantograph differential equations: Taylor operational matrix method

Author(s): Nikita Saha, Randhir Singh

Pages: 2563 - 2579

5) L-fuzzy transforms: an operator-oriented approach

Author(s): A. P. Singh, S. P. Tiwari, I. Perfilieva

Pages: 2581 - 2593

6) A golden section-based group decision-making approach to software trustworthiness evaluation

Author(s): Chuan Yue

Pages: 2595 - 2618

7) The impact of hydrogen energy storage aqua electrolyzer fuels cell on automatic generation control of power system using optimal FGS PID controller

Author(s): Ankur Rai, Dushmanta Kumar Das

Pages: 2619 - 2638

8) Choquet integral in ranking data: on the construction of a measure of importance and interaction

Author(s): M. Eugenia Cornejo, Jesús Medina, Andreja Tepavčević

Pages: 2639 - 2651

9) Applications of integrals and extreme value of solution of uncertain age-dependent population equation with migration source

Author(s): Lu Yang

Pages: 2653 - 2668

10) A modified slacks-based measure of efficiency and super-efficiency under zero and negative data

Author(s): Ehsan Zanboori

Pages: 2669 - 2686

11) Optimal stress levels and inference procedures for constant stress accelerated life test under bathtub-shaped lifetime model

Author(s): Çağatay Çetinkaya

Pages: 2687 - 2714

12) Fc-gcn: A formal concept-enhanced graph convolution network model

Author(s): Kai Wu, Chao Zhang, Vincenzo Loia

Pages: 2715 - 2725

13) A model-free feature extraction procedure for interval-valued time series prediction

Author(s): Wan Tian, Zhongfeng Qin, Tao Hu

Pages: 2727 - 2741

14) Neutrosophic multi-choice 4D-transportation problem for different quality items

Author(s): Dipankar Chakraborty, Sarbari Samanta, Dipak Kumar Jana

Pages: 2743 - 2767

15) Optimizing energy harvesting in web of things services: a metaheuristic approach with retrial queue under working vacation

Author(s): N. Micheal Mathavavisakan, K. Indhira, Sherif I. Ammar

Pages: 2769 - 2790

16) Differentiation or undifferentiation? analysis of car-sharing strategies for the vehicle manufacturer

Author(s): Xin Yu, Zhongwei Chen, Zhi-Ping Fan

Pages: 2791 - 2806

17) A two-stage optimization replacement policy with multiple spare units

Author(s): Chunxiao Zhang, Hejiao Shen, Chao Yan

Pages: 2807 - 2817

18) A new model for facility bus terminal location problem based on modified Kerre’s inequality

Author(s): Sahar Rahdar, Reza Ghanbari, Donya Heidari

Pages: 2819 - 2828

19) A new metaheuristic optimization algorithm based on the participation of smart students to increase the class performance

Author(s): Einollah Pira, Alireza Rouhi

Pages: 2829 - 2844

20) A novel stochastic machine learning approach for resilient-leagile supplier selection: a circular supply chain in the era of industry 4.0

Author(s): Bahar Javan Molaei, Mohssen Ghanavati-Nejad, Mohammad Sheikhalishahi

Pages: 2845 - 2866

21) An arithmetic–geometric mean difference based approach to consistency index and priority vector of pairwise comparison matrices

Author(s): Yuan-Kai Hu, Fang Liu, Shi-Shan Wang

Pages: 2867 - 2884

22) On pure ideals in semilattices

Author(s): Nilesh Mundlik, Mayur Kshirsagar

Pages: 2885 - 2889

23) Innovative image encryption approach based on bitwise XOR high nonlinear S-boxes and random permutation

Author(s): Fırat Artuğer

Pages: 2891 - 2903

24) Evolutionary optimization in VANET services: a comprehensive survey, challenges and futuristic approach

Author(s): Madhuri Badole, Anuradha Thakare, Diego Oliva

Pages: 2905 - 2929

25) Wind farm layout optimization based on Harris hawk optimization algorithm with variable weight coefficients and Jansen wake model

Author(s): Min Wang, Jie-Sheng Wang, Yu-Cai Wang

Pages: 2931 - 2969

26) Construction and empirical research of a subjective-and-objective-analysis model of the online learning behavior

Author(s): Ke Wang, Kun Zheng, Ying Wang

Pages: 2971 - 2982

27) A synchronous spatiotemporal graph neural network for short-term traffic flow prediction

Author(s): Zhao Zhang, Xiaohong Jiao

Pages: 2983 - 2997

28) Modeling of metaheuristic-based dual cluster head selection with routing protocol for energy-efficient wireless sensor networks

Author(s): Maddikera Krishna Reddy, Anusha Sowbarnika Veluswamy, Syed Shameem

Pages: 2999 - 3020

29) Expansive detector via hybrid temporal and transposed convolutional mechanism for weld proximity defects

Author(s): Zihua Chen, Runmei Zhang, Kuan-ching Li

Pages: 3021 - 3034

30) Forecasting of exchange rate time series based on event-aware transformer mode

Author(s): Siyi Zhang, Tong Che, Ping Feng

Pages: 3035 - 3045

31) Sustainability, innovation and knowledge: a complex relationship based on an empirical study

Author(s): Sebastian-Ion Ceptureanu, Eduard-Gabriel Ceptureanu, Adriana Lavinia Iancu

Pages: 3047 - 3062

32) Why does economics need complexity?

Author(s): Mauro Gallegati, Silvia Gallegati

Pages: 3063 - 3072

33) A review for finding determinants of some band matrices

Author(s): Maryam Shams Solary

Pages: 3073 - 3082

34) Modeling and simulating a startup ecosystem development with a delayed differential equation

Author(s): Alessio Brini, Viviana Fanelli

Pages: 3083 - 3095

35) Explainable Grouped Deep Echo State Network for EEG-based emotion recognition

Author(s): Samar Bouazizi, Hela Ltifi

Pages: 3097 - 3114

[mpboardsolutions-blog]

MP Board Class 12th Maths Book Solutions in English Medium

MP Board Class 12th Maths Chapter 1 Relations and Functions

Chapter 1 Relations and Functions Ex 1.1

Chapter 1 Relations and Functions Ex 1.2

Chapter 1 Relations and Functions Ex 1.3

Chapter 1 Relations and Functions Ex 1.4

Chapter 1 Relations and Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 2 Inverse Trigonometric Functions

Chapter 2 Inverse Trigonometric Functions Ex 2.1

Chapter 2 Inverse Trigonometric Functions Ex 2.2

Chapter 2 Inverse Trigonometric Functions Miscellaneous Exercise

MP Board Class 12th Maths Chapter 3 Matrices

Chapter 3 Matrices Ex 3.1

Chapter 3 Matrices Ex 3.2

Chapter 3 Matrices Ex 3.3

Chapter 3 Matrices Ex 3.4

Chapter 3 Matrices Miscellaneous Exercise

MP Board Class 12th Maths Chapter 4 Determinants

Chapter 4 Determinants Ex 4.1

Chapter 4 Determinants Ex 4.2

Chapter 4 Determinants Ex 4.3

Chapter 4 Determinants Ex 4.4

Chapter 4 Determinants Ex 4.5

Chapter 4 Determinants Ex 4.6

Chapter 4 Determinants Miscellaneous Exercise

MP Board Class 12th Maths Chapter 5 Continuity and Differentiability

Chapter 5 Continuity and Differentiability Ex 5.1

Chapter 5 Continuity and Differentiability Ex 5.2

Chapter 5 Continuity and Differentiability Ex 5.3

Chapter 5 Continuity and Differentiability Ex 5.4

Chapter 5 Continuity and Differentiability Ex 5.5

Chapter 5 Continuity and Differentiability Ex 5.6

Chapter 5 Continuity and Differentiability Ex 5.7

Chapter 5 Continuity and Differentiability Ex 5.8

Chapter 5 Continuity and Differentiability Miscellaneous Exercise

MP Board Class 12th Maths Chapter 6 Application of Derivatives

Chapter 6 Application of Derivatives Ex 6.1

Chapter 6 Application of Derivatives Ex 6.2

Chapter 6 Application of Derivatives Ex 6.3

Chapter 6 Application of Derivatives Ex 6.4

Chapter 6 Application of Derivatives Ex 6.5

Chapter 6 Application of Derivatives Miscellaneous Exercise

MP Board Class 12th Maths Chapter 7 Integrals

Chapter 7 Integrals Ex 7.1

Chapter 7 Integrals Ex 7.2

Chapter 7 Integrals Ex 7.3

Chapter 7 Integrals Ex 7.4

Chapter 7 Integrals Ex 7.5

Chapter 7 Integrals Ex 7.6

Chapter 7 Integrals Ex 7.7

Chapter 7 Integrals Ex 7.8

Chapter 7 Integrals Ex 7.9

Chapter 7 Integrals Ex 7.10

Chapter 7 Integrals Ex 7.11

Chapter 7 Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 8 Application of Integrals

Chapter 8 Application of Integrals Ex 8.1

Chapter 8 Application of Integrals Ex 8.2

Chapter 8 Application of Integrals Miscellaneous Exercise

MP Board Class 12th Maths Chapter 9 Differential Equations

Chapter 9 Differential Equations Ex 9.1

Chapter 9 Differential Equations Ex 9.2

Chapter 9 Differential Equations Ex 9.3

Chapter 9 Differential Equations Ex 9.4

Chapter 9 Differential Equations Ex 9.5

Chapter 9 Differential Equations Ex 9.6

Chapter 9 Differential Equations Miscellaneous Exercise

MP Board Class 12th Maths Chapter 10 Vector Algebra

Chapter 10 Vector Algebra Ex 10.1

Chapter 10 Vector Algebra Ex 10.2

Chapter 10 Vector Algebra Ex 10.3

Chapter 10 Vector Algebra Ex 10.4

Chapter 10 Vector Algebra Miscellaneous Exercise

MP Board Class 12th Maths Chapter 11 Three Dimensional Geometry

Chapter 11 Three Dimensional Geometry Ex 11.1

Chapter 11 Three Dimensional Geometry Ex 11.2

Chapter 11 Three Dimensional Geometry Ex 11.3

Chapter 11 Three Dimensional Geometry Miscellaneous Exercise

MP Board Class 12th Maths Chapter 12 Linear Programming

Chapter 12 Linear Programming Ex 12.1

Chapter 12 Linear Programming Ex 12.2

Chapter 12 Linear Programming Miscellaneous Exercise

MP Board Class 12th Maths Chapter 13 Probability

Chapter 13 Probability Ex 13.1

Chapter 13 Probability Ex 13.2

Chapter 13 Probability Ex 13.3

Chapter 13 Probability Ex 13.4

Chapter 13 Probability Ex 13.5

Chapter 13 Probability Miscellaneous Exercise

[meritbatch]

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

[vectoralgebraclass12]

Lecture -1 Vector Algebra Class 12 Maths Chapter 10

NCERT Exercise 10.1 Vector Algebra Class 12 Maths 

NCERT Exercise 10.2 Vector Algebra Class 12 Maths

How to study Vector Algebra & Three-Dimensional Geometry?

Vector Algebra Class 12 Maths

Vector Algebra Class 12 Assignments

Full Syllabus of Class 12 Maths

[ashishkumarletslearn]

Vector Algebra Class 12 Maths IIT JEE Mains

Detailed explanation of vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors including basics to advance level concepts, NCERT Solutions, R.D Sharma, R.S Aggarwal, Important Examples from the boards point of view for NCERT Chapter 10 Vector Algebra Class 12 Maths IIT JEE Mains.

Below is the list of High-Quality Video Lectures links for Vector Algebra Class 12 Maths:

Lecture -1 Vector Algebra Class 12 Maths Chapter 10

NCERT Exercise 10.1 Vector Algebra Class 12 Maths

NCERT Exercise 10.2 Vector Algebra Class 12 Maths

How to study Vector Algebra & Three Dimensional Geometry?

[cbse-board]

Detailed explanation of ‘how to represent vectors, types of vectors and ncert solutions for Exercise 10.1 of Chapter 10 Vector Algebra Class 12 Maths.

#VectorAlgebra #Class12Maths

[jackdockymine]

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[fuelcut]

Silicon Valley’s imaginary Q2 2020 earnings call

[switch to long version]

CEO, MEGA TECH CORP - Hello everyone. These aren’t normal times. We’re not going to talk about our 10Q on this call. We’re here to talk about the next 10 years. So if you’re here for DAUs, ARR or CPC, you can drop off now.

We’ve been doing a lot of thinking about the race, health and economic crises our country faces. Over the last few weeks, I’ve asked our exec team to leave their homes, their [Zoom alternative] calls and their DoorDash deliveries to join protests and explore our community through new eyes.

What we now see - more clearly than ever - is that our entire company, industry, and Valley - are built on flawed foundations. A flawed social contract.

We can no longer just focus on the magical software bits and hope someone else figures out racial equity, employment, climate and health. This is Joel Spolsky’s Law of Leaky Abstractions on the ultimate scale. The abstractions are failing - and we’re seeing bugs and unintended consequences all around us. And the more we invest to deal with one-off bugs, the more likely we are to calcify change and imprison ourselves inside a failing stack. It’s like we decided to build the world’s notification service on Ruby on Rails - or building an iPhone competitor on Windows CE. Fail Whale everywhere. Unfortunately, America’s democratic institutions are in poor condition. They are struggling to deal with inequality let alone looming environmental disaster.  A polarized electorate - particularly at the national level - leads to populism and makes it hard for these institutions to execute meaningful, long-term plans.

We talk a lot about speech, misinformation, fairness of targeted ads etc. But it’s becoming clear that UX, linear algebra/training data and monetization in our products is just the tip of the spear to address polarization. We believe polarization is a product of the underlying conditions of civil rights, education, health and climate debt that affect Americans differentially based on race, wealth, neighborhood and region. 

So will today’s peaceful protests for racial justice expand into tomorrow’s revolution(s) for economic freedom? If you don’t think things are bad now, think about what happens when the stimulus checks run out. Take a look at the amount of debt in the public sector, use any imagination about COVID, work out what happens to their tax base / pension returns and consider the impact on public services, public servants and their votes.  MMT better be a real thing. Maybe we didn’t start these fires, but that refrain won’t save us when the flames come our way.

We’re done debating why we need to act. It’s clear America needs our help. Let’s talk about how we’re going to rise to the occasion. Our mantra will be “internalize, innovate, institutionalize”.

First, we’re going to internalize our problems. I’m here to tell you that issues of racial and economic justice are not just moral issues but they’re financial issues. Racial debt, education debt, health debt, climate debt  will hit us harder and harder each year.  (By the way, revolution probably won’t be great for your DCF models.) So we’re going to recognize these off-balance sheet liabilities - which amount to a few hundred billion in the US alone over the next 10 years for a company at our scale. You should assume other CEOs are thinking the same things - even if it takes them a few more quarters or years to say it.  

Second, we’re going to innovate against these systemic problems - but our only shot at making progress is if we realign the entire company’s mission to address them. This is not about optics. This is not about philanthropy. This is not another bet.  We have no choice but to put all our chips behind one bet - America - at least to start. It's the country that backed us in the first place, it's where most of our people are and most of our profits. The job for our existing products, platforms and cash flows will be to advance four areas: place / race, skilling / manufacturing, health / food and climate / mobility - starting in America. The board will measure me based on job creation and diversity.  It should go without saying that we’re pausing dividends and buybacks for the foreseeable future. Every dollar will serve our mission. Every senior leader will need to sign up for our new mission - and those who choose to stay will receive a new, back-end loaded, 10 year vesting schedule.  We want them focused on the long-term health of society - not the whims of Robinhood day traders or strengthening the moats of existing products. We will need to invent entirely new ways to operate and ship products. As Joel Spolsky said, “when you need to hire a programmer to do mostly VB programming, it’s not good enough to hire a VB programmer, because they will get completely stuck in tar every time the VB abstraction leaks”. We need engineers, designers and product managers that will look deep into the stack, confront the racial, job access, health and climate debts that our products, our companies and our communities are built on top of.   This is not about CYA process to protect cash cows or throwing things over the fence to policy. We will need to innovate across technical, cultural and organizational lines. This requires deep understanding and curiosity. Systems and full-stack, not just pixels. This will bring more scrutiny to our company - not less.  Change must not be the burden for only our Black employees or other subsets. Everyone must be on board - so for the next 12 months, we’re giving folks a one-time buyout if they want to leave.

Third, we can’t do any of this by ourselves.  The problems are too big. Our role will be to provide enlightened risk capital (from our balance sheet or by re-vectoring operating spend) alongside R&D, product, platform leverage to help leaders and innovators pursue solutions in these areas. We will work with our peers and the public sector wherever possible - buying/R&D consortia, public-private partnerships, trusts, etc. Collaboration is the default, not the exception. But the new era and landscape demands that we explore institutional models beyond global capital/startups, labor unions, NGOs or government. We need models that can more flexibly align people and purpose, that innovate on individualized vs. socialized risk/reward - and that ultimately help build and sustain local, social capital. It’s difficult to say what these will look like - but increasingly figuring this out will be existential for our core business. Right now, it doesn’t matter if you’re designing the best cameras in Cupertino or the best ways to see their snaps in Santa Monica - we’re all just building layers of an attention stack for global capital. Our Beijing competitors have figured this out. ByteDance is already eating our lunch. They’re using the same tech inputs as us - UX, ML and large-scale systems - which are now a commodity - but with vastly lower consequences for the content they show - creating a superior operating / scaling model. They’re not internalizing social or political cost. What we need in this era is the accumulation stack - where each interaction builds social capital.  This is not about global likes. This is about local respect. We’ll create competitive advantage when we build products that reach across race / economic lines to harness America’s amazing melting pot and do so in ways that build livelihoods / property rights for creators and stakeholders.

With this operating model in place, we’re committing to fundamental change in four areas:

Place & Race - Over the next 10 years, 100% of our jobs will be in diverse communities that embrace inclusive schooling, policing, housing and transit policies. (Starting tomorrow, we’re putting red lines on our maps around towns with exclusionary zoning.) This is not about privatizing cities or an HQ2-style play to extract concessions. This is about investing our risk capital and our reputation to innovate alongside government. How do we bring world-class education to neighborhoods with concentrated poverty? What is the future of digital/hybrid charter schooling? Unbundled public safety? We’re done with de facto segregation. We’ll embrace “remote-first” with physical centers of gravity as a means to this end. The Bay will become one physical node alongside several others (e.g. Atlanta, DC, LA) creating a strategic network to develop diverse talent across the country. We’re going to coordinate our investment with leading peers - since after all, this isn’t about cost or cherry-picking. It’s about broadening our country’s economic base.

Skilling & Manufacturing - We’re going to 10x the tech talent pool in 10 years - by inventing new apprenticeship models that bring women, minorities and the poor into the workforce. We’ll start with our existing contractor base, convert them to new employment models with expanded benefits and paths for upward mobility. Next, we will invent new productivity tools for all types of workers - from the front office to mobile work to call center - that brings the power of AI and programming to everyone. These will be deeply tied into new platforms for work designed from the bottom-up to build social and financial capital for individual workers and teams. Last, we’re setting a goal to manufacture most of our hardware products - from silicon all the way to systems - entirely in the US in 10 years. This will require massive investment, collaboration and innovation. It may require a revolution in robotics - but we will pursue this in a way that makes the American worker competitive - not a commodity to be automated away. If we’re successful, the dividends of our investment here will have massive spillover benefits to every other sector of manufacturing in the US - autos, etc. - including ones we have yet to dream up.

Health & Food -  We’re not going to tolerate a two-class system for healthcare. As we convert our contract workforce to new employment models, we’ll innovate on the fundamental quality/cost paradigm. This may feel like a step down but it will put us (and the rest of society if we’re successful) on a fundamentally better long-term trajectory. Can we use AI to help scale the reach of community health workers? Can we help them create co-operatively owned care delivery orgs that offer new ways to share risk and support behavior change?  Local, social capital is critical. Food is part of Health, and we’re going to innovate there too. Free food for employees is not going to come back post-COVID. Instead, we’ll use our food infrastructure to bootstrap cooperatively-owned cloud kitchens. We’ll provide capital to former contractors - mostly Black and Hispanic - to invest and own these. We’ll build platforms to help them sell food to employees (partly subsidized), participate in new “food for health” programs and eventually disrupt the extractive labor practices we see across food, grocery and delivery.

Climate & Mobility - Lastly, we’ll be imposing a carbon tax on all aspects of our own operations - which we’ll use to “fund” innovation in this space - with a primary focus on job creation. This is an area where we’re going to be looking far beyond our four walls from the beginning.  As a first step, we’re teaming up with Elon and Gavin Newsom to buy PG&E out of bankruptcy and restructure it as a 21st century “decentralized” network of community utilities.  It will accelerate the electrification of mobility - financing networked batteries for buses, cars and bikes along with charging infrastructure - and lead a massive job creation program focused on energy efficiency. It will use its rights of way to provide Gigabit ethernet + 5G to everyone - which will help people and help fund some of this.  Speaking of mobility, private buses aren’t coming back after COVID. Instead, we’re teaming up with all of our peers to create a Bay-wide network of electric buses (with bundled e-bikes) that will service folks of all walks of life - including our own employee base. Oh and one more thing - we’re bringing together the world’s most advanced privacy/identity architecture and computational video/audio to bake public health infrastructure directly into the buses. For COVID and beyond. None of this is a substitute for competent, democratically accountable regional authorities. This is us investing risk capital on behalf of society - with the goal of empowering these authorities.

Open technology for global progress - While we have to prioritize America given the scale of problems, the intent is not to abandon the rest of the world or hold back it’s progress. We feel the opposite - that over the coming decades each country’s technology sectors will thrive. To get there, we will continue to invest patiently - hiring, training, partnering, investing and innovating - but with a clear north star to help each country develop local leaders in new areas. Long-term, we’ll continue to contribute open technology that others can build upon.

America should be the proverbial city on a hill for everyone - not a metaverse for the rich with the poor dying in the streets. We don’t have much time so we’re getting to work now. See you next quarter.

[valpy-blog]

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4

NCERT Solutions for Class 12th Maths Chapter 10 Vector Algebra Ex 10.4

Get Free NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Ex 10.4 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Vector Algebra Exercise 10.4 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of…

[anushacbse]

CBSE Class 12 Maths Revision Notes

Class 12 Maths Notes: Class 12 Maths Notes is designed to help for the students who are going to appear final exams, students can read this CBSE Class 12 Maths Revision Notes before going to exam to cover all chapters and topics in last minute and can easily revise all chapters of class 12 Maths. Important topics like Trigonometry, integrals, equations and three-dimensional geometry has been included in Class 12 Maths Notes. For CBSE Students board exams will be conducted by NCERT. Class 12 Maths Notes has been designed on the basis of the latest NCERT syllabus textbooks. So students can check CBSE Class 12 Maths Quick Revision Notes and can download the solutions in PDF’s format as well. Students can practice the Class 12 Maths Revision Notes to gain more knowledge.

Class 12 Maths consists of 13 Chapter below is the list of chapter Names.

Chapter 1: Relations and Functions Chapter 2: Inverse Trigonometric Functions Chapter 3: Matrices Chapter 4: Determinants Chapter 5: Continuity and Differentiability Chapter 6: Application of Derivatives Chapter 7; Integrals Chapter 8: Application of Integrals Chapter 9: Differential Equations Chapter 10: Vector Algebra Chapter 11: Three Dimensional Geometry Chapter 12: Linear Programming Chapter 13: Probability

Students can download the PDF’s of Class 12 Maths Revision Notes. The Class 12 Maths Notes will also help in understanding the chapters properly as it will contain the important points for revision purpose in short times

[vectoralgebraclass12]

Vector Algebra is a one of the basic topics that is necessary to understand the various concepts of Physics and Mathematics. Vector Algebra is the prerequisite for concepts like Kinematics and basics for students intended to go for engineering studies like IIT JEE Mains, other entrances, boards, and higher studies in Mathematics. It covers all the basic to advance concepts, each NCERT Solutions, R.D Sharma, R.S Aggarwal, Board’s Question Bank, Important Examples and Comprehensive Educational Resources for Vector Algebra Class 12 Maths including Assignments and high-quality video lectures prepared by expert teacher from the boards point of view.

Vector Algebra Class 12 Maths

[ashishkumarletslearn]

#VectorAlgebra #Class12Maths #IITJeeMains

Detailed explanation of Vector algebra and how to represent a vector in maths explained by expert teacher for Class 12 Maths.