NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra (Ex 10.1) Exercise 10.1
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Mathematics is purely conceptual and includes complicated calculations; therefore, scoring well in the subject can be challenging for students. Class 12 Mathematics curriculum offers a wide range of new chapters to students and includes multiple properties, operations, and much more. It is difficult for the students to comprehend all these concepts and perform well in the Class 12 board examinations. Therefore, Extramarks provides students with the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1, NCERT Solutions, sample papers, past years’ papers and much more so that students can have access to complete and credible study material for their examinations.
Sample papers and past years’ papers are one of the most important tools for the preparation of students. They provide students with a model of the examination pattern as well as the chapter weighting and the marking scheme of the board examination. Extramarks recommends students go through a number of sample papers and past years’ papers before their examinations.
Along with NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1, Extramarks also provides students with NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 9, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 6, NCERT Solutions Class 5, NCERT Solutions Class 4, NCERT Solutions Class 3, NCERT Solutions Class 2 and NCERT Solutions Class 1. Therefore, students of all the classes can have access to the study material of all the subjects.
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra (Ex 10.1) Exercise 10.1
Chapter 10 of Class 12 Mathematics is Vector Algebra. It can be the most scoring chapter of Class 12 Mathematics. Vector Algebra is based on the concepts of the Algebra of Vector Quantities. Furthermore, there are two types of physical quantities – scalar, and vector quantities. Scalar quantities just have magnitude. Vector quantities have both magnitude and direction.
The chapter includes Introduction, Some Basic Concepts, Types of Vectors, Addition of Vectors, Multiplication of Vector by a Scalar, Components of a Vector, Vector Joining Two Points, Section Formula, Product of Two Vectors, Scalar Product of Two Vectors, Projection of a Vector on a Line and Cross Product of two Vectors. Class 12 Maths 10.1 is based on the topics Introduction, Basic conceptsPosition Vector and Direction Cosines. The Exercise contains five questions and helps students to clear their basic concepts of the chapter.
Extramarks provides students with complete and comprehensive study material so that they can score well in the board examinations.
In addition to NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1, Extramarks provides students with a variety of learning modules that aid in a systematic and enjoyable learning process.Multiple learning modules such as LearnPracticeTest pedagogy, K12 study material, curriculum mapping, complete syllabus coverage, and much more help students succeed in any inschool, board, or competitive examination. They allow students to learn flexibly, anytime, and anywhere. They also help students with selfassessment to track their academic progress and preparation level.. The Learning App also helps young minds learn effectively at their own pace and allows them to take short breaks between their classes. This way, students enjoy learning and do not feel that learning is monotonous. In addition, students can clear their doubts anytime, which helps them with indepth knowledge and clarified concepts. The Extramarks’ website provides students with comprehensive courses that are more affordable and also comfortable for everyone. Also, it provides students with all the resources that are required for the preparation of the board examinations, such as the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1. Extramarks is a onestop solution for all the problems of the students, as it brings the classes of all the subjects to one place.
Access NCERT Solutions for Class12 Maths Chapter 10 – Vector Algebra
Class 12 students can not spend their time looking for answers on different sites. Extramarks provides them with reliable and authentic study material without having to search anywhere else. The NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 provided by Extramarks are curated by expert educationalists and are properly detailed in a stepbystep approach. Also, students can easily access the solutions of Ex 10.1 Class 12 as they are available in PDF format.
NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.1
There are numerous benefits of the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 provided by the Extramarks’ website. The Class 12 Math board examination can be difficult for students to pass because the question paper is of a higher level.Students require meticulous practise to have the curriculum of Class 12 Mathematics at their fingertips. The first and foremost step to obtaining good scores in Class 12 Mathematics is to practise the NCERT Textbook solutions, like NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1. However, the NCERT Textbooks do not contain the solutions to the questions incorporated in them, therefore, it is essential for the students to have a readymade study material. Furthermore, having a clear understanding of the concepts is very crucial for the students in Class 12.Therefore, Extramarks provides students with the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 so that they can have credible study material and can perform efficiently in their academics.
Students can sometimes miss their classes and have doubts about the subject’s curriculum. Therefore, Extramarks provides them with NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 so that they do not miss out on any important questions and can be able to easily solve their queries. The NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 provided by Extramarks, provides students with an idea about the pattern in which the answers should be written in the board examinations. Students can easily master the fundamentals of the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 as they have previously gone through the concepts of the topic in the past academic years. Students can refer to the Extramarks’ website for access to the stepbystep explanation of NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1. Extramarks is a website that provides students with all the resources they need to do well in their board examinations. The NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 provided by Extramarks walk students through each step of the problem and help them understand the logic behind it.Practising these solutions helps students gain a better understanding of the concepts in the chapter. These solutions are not only helpful in scoring well in board examinations but are also very helpful in competitive examinations. . Also, Vector Algebra is an important concept in the field of Physics. For a better grasp of the curriculum of the chapter, students are required to have a thorough practise of the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 as well as the extra questions on the topics. Students can use the Extramarks website to find NCERT textbook solutions as well as other practise assignments to help them do well in the board exams.It is critical for students to prepare for their board exams by having access to accurate, detailed, and wellexplained NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1.NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1 Frequently Asked Questions
Q.1 Represent graphically a displacement of 40 km, 30° east of north.
Ans
$\begin{array}{l}\text{Here},\text{\hspace{0.17em}}\mathrm{vector}\text{}\overrightarrow{\mathrm{OP}}\text{represents the displacement of 40 km, 30\xb0}\\ \text{East of North.}\end{array}$
Q.2 Classify the following measures as scalars and vectors.
(i) 10 kg
(ii) 2 meters northwest
(iii) 40°
(iv) 40 watt
(v) 10^{19} coulomb
(vi) 20 m/s^{2}
Ans
(i) 10 kg is a scalar quantity because it involves only magnitude.
(ii) 2 meters northwest is a vector quantity as it involves both magnitude and direction.
(iii) 40° is a scalar quantity as it involves only magnitude.
(iv) 40 watts is a scalar quantity as it involves only magnitude.
(v) 10^{–19} coulomb is a scalar quantity as it involves only magnitude.
(vi) 20 m/s^{2} is a vector quantity as it involves magnitude as well as direction
Q.3 Classify the following as scalar and vector quantities.
(i) time period
(ii) distance
(iii) force
(iv) velocity
(v) work done
Ans
(i) Time period is a scalar quantity as it has only magnitude.
(ii) Distance is a scalar quantity as it has only magnitude.
(iii) Force is a vector quantity as it has both magnitude and direction.
(iv) Velocity is a vector quantity as it has both magnitude as well as direction.
(v) Work done is a scalar quantity as it has only magnitude.
Q.4 In fig.(a square), identify the following vectors.
(i) Coinitial
(ii) Equal
(iii) Collinear but not equal
Ans
$\begin{array}{l}\text{(i) Vectors}\overrightarrow{\mathrm{a}}\text{\hspace{0.17em}\hspace{0.17em}and}\overrightarrow{\mathrm{d}}\text{\hspace{0.17em}are coinitial because they have the same\hspace{0.17em}initial point.}\\ \text{(ii) Vectors}\overrightarrow{\mathrm{b}}\text{\hspace{0.17em}and}\overrightarrow{\mathrm{d}}\text{\hspace{0.17em}\hspace{0.17em}are equal because they have the same magnitude and direction.}\\ \text{(iii) Vectors}\overrightarrow{\mathrm{a}}\text{\hspace{0.17em}\hspace{0.17em}and}\overrightarrow{\mathrm{c}}\text{\hspace{0.17em}are collinear but not equal. This is because although they are parallel,}\\ \mathrm{their}\mathrm{directions}\mathrm{are}\mathrm{not}\mathrm{the}\mathrm{same}\text{.}\end{array}$
Q.5
$\text{Answer the following as true or false.}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\begin{array}{l}\left(\mathrm{i}\right)\hspace{0.17em}\hspace{0.17em}\overrightarrow{\mathrm{a}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{and}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\overrightarrow{\mathrm{a}}\mathrm{\hspace{0.17em}}\mathrm{are}\mathrm{collinear}.\\ \left(\mathrm{ii}\right)\mathrm{Two}\mathrm{collinear}\mathrm{vectors}\mathrm{are}\mathrm{always}\mathrm{equal}\mathrm{inmagnitude}.\\ \left(\mathrm{iii}\right)\mathrm{Two}\mathrm{vectors}\mathrm{having}\mathrm{same}\mathrm{magnitude}\mathrm{are}\mathrm{collinear}.\\ \left(\mathrm{iv}\right)\mathrm{Two}\mathrm{collinear}\mathrm{vectors}\mathrm{having}\mathrm{the}\mathrm{same}\mathrm{magnitude}\\ \hspace{0.17em}\mathrm{are}\mathrm{equal}.\end{array}$
Ans
(i) True. Since, both vectors are parallel to same line.
(ii) False.
Collinear vectors are those vectors that are parallel to the same line, irrespective of their magnitudes and directions.
(iii) False.
Collinear vectors are those vectors that are parallel to the same line, irrespective of their magnitudes and directions.
(iv) False.
Collinear vectors are those vectors that are parallel to the same line, irrespective of their magnitudes and directions.
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FAQs (Frequently Asked Questions)
1. Are the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 available on Extramarks?
Yes, the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 are available on the Extramarks’ website. Along with this, the website also provides students with various learning tools like indepth performance reports, complete syllabus coverage and much more. Students can have a bright academic career if they choose Extramarks for their learning needs.
2. Is it important to practice all the questions of Exercise 10.1 Class 12 Maths?
Yes, it is essential for the students to practice all the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 in order to have a better understanding of the chapter. It is essential for students to be thorough with the concepts and the calculations of Mathematics to avoid small mistakes in the board examinations. Also, practising the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 increases the pace of the students which helps students to complete their examinations on time.
3. Are the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 difficult?
No, the NCERT Solutions Class 12 Maths Chapter 10 Exercise 10.1 are not difficult, however, they are written in an easytounderstand language and are properly detailed so that the concepts of the chapter can be readily understood by students. Also, every question contains different concepts, therefore it is important for the students to practice as many questions as possible to score well in the examinations.