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

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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

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

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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.