# NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra (Ex 10.1) Exercise 10.1

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.

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## 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 concepts-Position Vector and Direction Cosines. The Exercise contains five questions and helps students to clear their basic concepts of the chapter.

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### Access NCERT Solutions for Class-12 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 step-by-step 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 ready-made 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.

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Q.1 Represent graphically a displacement of 40 km, 30° east of north.

Ans

$\begin{array}{l}\text{Here},\text{\hspace{0.17em}}\mathrm{vector}\text{}\stackrel{\to }{\mathrm{OP}}\text{represents the displacement of 40 km, 30°}\\ \text{East of North.}\end{array}$

Q.2 Classify the following measures as scalars and vectors.

(i) 10 kg
(ii) 2 meters north-west
(iii) 40°
(iv) 40 watt
(v) 10-19 coulomb
(vi) 20 m/s2

Ans

(i) 10 kg is a scalar quantity because it involves only magnitude.
(ii) 2 meters north-west 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/s2 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

$\begin{array}{l}\text{(i) Vectors}\stackrel{\to }{\mathrm{a}}\text{\hspace{0.17em}\hspace{0.17em}and}\stackrel{\to }{\mathrm{d}}\text{\hspace{0.17em}are coinitial because they have the same\hspace{0.17em}initial point.}\\ \text{(ii) Vectors}\stackrel{\to }{\mathrm{b}}\text{\hspace{0.17em}and}\stackrel{\to }{\mathrm{d}}\text{\hspace{0.17em}\hspace{0.17em}are equal because they have the same magnitude and direction.}\\ \text{(iii) Vectors}\stackrel{\to }{\mathrm{a}}\text{\hspace{0.17em}\hspace{0.17em}and}\stackrel{\to }{\mathrm{c}}\text{\hspace{0.17em}are collinear but not equal. This is because although they are parallel,}\\ \mathrm{their}\mathrm{directions}\mathrm{are}\mathrm{not}\mathrm{the}\mathrm{same}\text{.}\end{array}$

Q.5

$\text{Answer the following as true or false.}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\begin{array}{l}\left(\mathrm{i}\right) \stackrel{\to }{\mathrm{a}} \mathrm{and} -\stackrel{\to }{\mathrm{a}}\mathrm{ }\mathrm{are}\mathrm{collinear}.\\ \left(\mathrm{ii}\right)\mathrm{Two}\mathrm{collinear}\mathrm{vectors}\mathrm{are}\mathrm{always}\mathrm{equal}\mathrm{inmagnitude}.\\ \left(\mathrm{iii}\right)\mathrm{Two}\mathrm{vectors}\mathrm{having}\mathrm{same}\mathrm{magnitude}\mathrm{are}\mathrm{collinear}.\\ \left(\mathrm{iv}\right)\mathrm{Two}\mathrm{collinear}\mathrm{vectors}\mathrm{having}\mathrm{the}\mathrm{same}\mathrm{magnitude}\\ \mathrm{are}\mathrm{equal}.\end{array}$

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.

## 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 in-depth 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 easy-to-understand 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.