NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Exercise 10.2 – CBSE Term II Free PDF Download

Exercise 10.2 of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on the following topics:

  1. Addition of Vectors
    • Properties of vector addition
  2. Multiplication of a Vector by a Scalar
    1. Components of a vector
    2. Vector joining two points
    3. Section formula

All these topics can be understood thoroughly by solving the problems given in this exercise. The solutions of all the problems of this exercise are given here.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2

Access Answers to NCERT Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2 Page Number 440

ncert sol Class 12 maths chapter 10 ex 2 1
ncert sol Class 12 maths chapter 10 ex 2 2
ncert sol Class 12 maths chapter 10 ex 2 3
ncert sol Class 12 maths chapter 10 ex 2 4
ncert sol Class 12 maths chapter 10 ex 2 5
ncert sol Class 12 maths chapter 10 ex 2 6
ncert sol Class 12 maths chapter 10 ex 2 7
ncert sol Class 12 maths chapter 10 ex 2 8

Access Other Exercises of Class 12 Maths Chapter 10

Exercise 10.1 Solutions 5 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

Miscellaneous Exercise On Chapter 10 Solutions 19 Questions

Access Answers to NCERT Class 12 Maths Chapter 10 Exercise 10.2

1. Compute the magnitude of the following vectors:

NCERT Solutions Class 12 Mathematics Chapter 10- image 9

Solution:

Given vectors are:

NCERT Solutions Class 12 Mathematics Chapter 10- image 10

2. Write two different vectors having same magnitude.

Solution:

NCERT Solutions Class 12 Mathematics Chapter 10- image 11

3. Write two different vectors having same direction.

Solution:

Two different vectors having same directions are:

Let us

NCERT Solutions Class 12 Mathematics Chapter 10- image 12

NCERT Solutions Class 12 Mathematics Chapter 10- image 13

4. Find the values of x and y so that the vectors NCERT Solutions Class 12 Mathematics Chapter 10- image 14are equal

Solution:

Given vectors
NCERT Solutions Class 12 Mathematics Chapter 10- image 15will be equal only if their corresponding components are equal.

Thus, the required values of x and y are 2 and 3 respectively.

5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).

Solution:

The scalar and vector components are:

The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as,

NCERT Solutions Class 12 Mathematics Chapter 10- image 16

NCERT Solutions Class 12 Mathematics Chapter 10- image 17Thus, the required scalar components are –7 and 6 while the vector components are

NCERT Solutions Class 12 Mathematics Chapter 10- image 186. Find the sum of the vectors

Solution:

Let us find the sum of the vectors:

NCERT Solutions Class 12 Mathematics Chapter 10- image 19

NCERT Solutions Class 12 Mathematics Chapter 10- image 207. Find the unit vector in the direction of the vector

Solution:

We know that

NCERT Solutions Class 12 Mathematics Chapter 10- image 21

NCERT Solutions Class 12 Mathematics Chapter 10- image 22

8. Find the unit vector in the direction of vector , where P and Q are the points

(1, 2, 3) and (4, 5, 6), respectively

Solution:

We know that,

NCERT Solutions Class 12 Mathematics Chapter 10- image 23

9. For given vectors, NCERT Solutions Class 12 Mathematics Chapter 10- image 24and NCERT Solutions Class 12 Mathematics Chapter 10- image 25, find the unit vector in the direction of the vector NCERT Solutions Class 12 Mathematics Chapter 10- image 26

Solution:

We know that,

NCERT Solutions Class 12 Mathematics Chapter 10- image 27

10. Find a vector in the direction of vector NCERT Solutions Class 12 Mathematics Chapter 10- image 28which has magnitude 8 units.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics Chapter 10- image 29

NCERT Solutions Class 12 Mathematics Chapter 10- image 30

11. Show that the vectorsNCERT Solutions Class 12 Mathematics Chapter 10- image 31are collinear.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics Chapter 10- image 32

Therefore, we can say that the given vectors are collinear.

12. Find the direction cosines of the vector NCERT Solutions Class 12 Mathematics Chapter 10- image 33

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics Chapter 10- image 34

13. Find the direction cosines of the vector joining the points A (1, 2, –3) and

B (–1, –2, 1) directed from A to B.

Solution:

We know that the

Given points are A (1, 2, –3) and B (–1, –2, 1).

Now,

NCERT Solutions Class 12 Mathematics Chapter 10- image 35

14. Show that the vector NCERT Solutions Class 12 Mathematics Chapter 10- image 36is equally inclined to the axes OX, OY, and OZ.

Solution:

Firstly,

NCERT Solutions Class 12 Mathematics Chapter 10- image 37

15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are NCERT Solutions Class 12 Mathematics Chapter 10- image 38 respectively, in the ratio 2:1

(i) internally

(ii) externally

Solution:

We know that

The position vector of point R dividing the line segment joining two points

P and Q in the ratio m: is given by:

NCERT Solutions Class 12 Mathematics Chapter 10- image 39

NCERT Solutions Class 12 Mathematics Chapter 10- image 40

16. Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).

Solution:

The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, – 2) is given by,

NCERT Solutions Class 12 Mathematics Chapter 10- image 41

17. Show that the points A, B and C with position vectors,NCERT Solutions Class 12 Mathematics Chapter 10- image 42NCERT Solutions Class 12 Mathematics Chapter 10- image 43respectively form the vertices of a right angled triangle.

Solution:

We know

Given position vectors of points A, B, and C are:

NCERT Solutions Class 12 Mathematics Chapter 10- image 44

Hence, proved that the given points form the vertices of a right angled triangle.

18. In triangle ABC (Fig 10.18) which of the following is not true:

NCERT Solutions Class 12 Mathematics Chapter 10- image 45

Solution:

Firstly let us consider,

NCERT Solutions Class 12 Mathematics Chapter 10- image 46

19. If NCERT Solutions Class 12 Mathematics Chapter 10- image 47are two collinear vectors, then which of the following are incorrect:

A. NCERT Solutions Class 12 Mathematics Chapter 10- image 48, for some scalar λ

B. NCERT Solutions Class 12 Mathematics Chapter 10- image 49

C. the respective components of NCERT Solutions Class 12 Mathematics Chapter 10- image 50are proportional

D. both the vectors NCERT Solutions Class 12 Mathematics Chapter 10- image 51have same direction, but different magnitudes

Solution:

We know

NCERT Solutions Class 12 Mathematics Chapter 10- image 52

NCERT Solutions Class 12 Mathematics Chapter 10- image 53

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class