Vector Algebra is one of the important concepts utilised in mathematics and physics, and NCERT solutions for class 12 chapter 10 elaborate on it. We do come across various questions in our daily lives, such as the height of a tree or, to put it in another way, how hard should a ball be hit to score a goal? The only thing that one can say in response to such questions is ‘Magnitude’ and such magnitudes are called scalars. However, if we also need to determine the direction in which a tree is growing or in what direction one must hit the ball to reach the goal, we must use another quantity known as a Vector.
Therefore, a vector is defined as a quantity with both direction and magnitude. We need scalars such as: length, mass, time, distance, speed, area, volume as well as vectors like displacement, velocity, acceleration, force, weight, both for Mathematics and Physical Science. NCERT Solutions for Class 12 Mathematics Chapter 10 demonstrates solutions with the use of vectors.
The problems in the NCERT Solutions for Class 12 Mathematics chapter 10 are based on real-life scenarios that help students understand the topic easily. The lesson begins with an overview of some basic vector concepts and builds on them to thoroughly explain more complex subjects. The best thing about the NCERT solutions for Class 12 Mathematics Chapter 10 vector algebra is that it conveys tough sections in vernacular and easy language so that it could easily be understood by students with different intellect levels.
Key Topics Covered in NCERT Solutions Class 12 Mathematics Chapter 10
The topics discussed in NCERT Solutions Class 12 Mathematics Chapter 10 are equally essential because they explain various sections of vectors, such as direction cosines, dot product, cross product, section formula, and associated properties. Furthermore, all topics are interconnected, implying that students cannot move on to the next section without first mastering the prior one. Therefore, studying each and every topic is necessary.
List of NCERT Solutions Class 12 Mathematics Chapter 10 Exercises
The word ‘Vector’ comes from ‘Vectus’, a Latin word, which means “to carry.” Modern vector theory began in 1800 when Caspar Wessel (1745-1818) and Jean Robert Argand (1768-1822) demonstrated how to use a directed line segment in a coordinate plane to give the geometric interpretation of a complex number. Mathematicians conducted additional research, culminating in the topic as we know it today. Below are links to NCERT solutions class 12 Mathematics chapter 10, offering highly engaging facts and recommendations to assist students in studying the subject matter with ease.
There are various lessons in both Mathematics and Physics that need students to have a solid understanding of vectors. As a result, you must regularly review the solutions in these links and take notes on all the procedures and formulas stated in them. NCERT Solutions for Class 12 Mathematics Chapter 10 Vector Algebra for each practice question is provided in the links below.
Class 12 Mathematics Chapter 10 – Ex 10.1 Solutions – 5 Questions
Class 12 Mathematics Chapter 10 – Ex 10.2 Solutions – 19 Questions
Class 12 Mathematics Chapter 10 – Ex 10.3 Solutions – 18 Questions
Class 12 Mathematics Chapter 10 – Ex 10.4 Solutions – 12 Questions
Class 12 Mathematics Chapter 10 Miscellaneous Ex – 19 Questions
Total Questions: There are 63 sums in Chapter 10 of Class 12 Mathematics Vector Algebra, divided into 20 simple computational questions, 37 medium-level problems, and 6 difficult problems.
NCERT Solutions Class 12 Mathematics Chapter 10 Formula List
All the formulas students need to understand this chapter are used in NCERT Solutions for class 12 Mathematics chapter 10 to help execute arithmetic operations on vectors. The same laws that apply to whole numbers or scalars do not apply to vectors, which have their direction. As a result, the computations for vectors alter when this element is taken into consideration.
Several geometrical implications of vectors are discussed in this chapter, which contains additional formulas and processes some of which are mentioned below.
- Let S and T be two given vectors; then the dot product is represented by S.T = |S| |T| cos θ.
- If θ = 0°, meaning both S and T are in the same direction, then T = |S| |T|.
- If θ = 90°, meaning S and T are orthogonal then T = 0.
- If we have two vectors S = (S1, S2, S3 ….. Sn) and T = (T1, T2, T3 ….. Tn) then the dot product is given as S.T = (S1T1 + S2T2 + S3T3 ….. SnTn)
Students should also create a chart on important formulae so that they can be accessed easily whenever needed.
NCERT Mathematics Syllabus
Class 12 NCERT Mathematics Syllabus
Term – 1
| Unit Name
|
Chapter Name |
|
Relations and Function |
Relations and Functions
Inverse Trigonometric Functions |
| Algebra
|
Matrices
Determinants |
| Calculus
|
Continuity and Differentiability
Application of Derivatives |
| Linear Programming |
Linear Programming |
Term – 2
| Unit Name |
Chapter Name |
|
Calculus
|
Integrals
Application of Integrals
Differential Equations |
| Vectors and Three-Dimensional Geometry |
Vector Algebra
Three Dimensional Geometry |
| Probability |
Probability |
Experts at Extramarks create NCERT Solutions to help students understand concepts more easily and precisely. NCERT Solutions provide detailed step-by-step explanations of problems found in textbooks. Solutions are available for various classes mentioned in the below links-
- NCERT Solutions class 1
- NCERT Solutions class 2
- NCERT Solutions class 3
- NCERT Solutions class 4
- NCERT Solutions class 5
- NCERT Solutions class 6
- NCERT Solutions class 7
- NCERT Solutions class 8
- NCERT Solutions class 9
- NCERT Solutions class 10
- NCERT Solutions class 11
- NCERT Solutions class 12
NCERT Mathematics Exam Pattern
| Duration of Marks |
3 hours 15 minutes |
| Marks for Internal |
20 marks |
| Marks for Theory |
80 marks |
| Total Number of Questions |
38 Questions |
| Very short answer question |
20 Questions |
| Short answer questions |
7 Questions |
| Long Answer Questions (4 marks each) |
7 Questions |
| Long Answer Questions (6 marks each) |
4 Questions |
NCERT Exemplar Class 12 Mathematics
NCERT Exemplar Class 12 Mathematics are available and can be accessed from NCERT official website. NCERT Exemplar Class 12 Mathematics Chapter 10 consists of problems with their solutions to help students prepare for their final exams. These Exemplar questions are a little more complex, and cover all the important concepts in Class 12 Mathematics Chapter 10. Students will fully understand all the concepts covered in chapter 10 by practising these NCERT Exemplars for Mathematics Class 12.
Introduction to vectors, types of vectors, addition and multiplication of vectors, vector components, section formula, scalar product, projection of a vector on a line, and vector product are all covered here. Each question in these materials is connected to topics covered in the CBSE Class 12 syllabus.
Key Features of NCERT Solutions Class 12 Mathematics Chapter 10
NCERT Solutions for Class 12 Mathematics are not only easy to comprehend, but they also include essential practice questions based on the recent CBSE syllabus.
The following are the important aspects to consider:
- You would be better positioned to clear your doubts because it provides in-depth knowledge in simple language.
- It simplifies and categorises every concept in the topic, making it easier to grasp.
- It offers multiple concepts for approaching the question paper and is based on CBSE pattern.
- These answers are a result of extensive research and are designed to lay the groundwork for your future studies.