NCERT Solution Class 12 Chapter 10- Vector Algebra Exercise 10.2

The 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 is given here.

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

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

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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 of Maths NCERT Class 12 Chapter 10.2

1. Compute the magnitude of the following vectors:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 1

Solution:

Given vectors are:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 2

2. Write two different vectors having same magnitude.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 3

3. Write two different vectors having same direction.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 4

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 5

4. Find the values of x and y so that the vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 6are equal

Solution:

Given vectors 
NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 7will 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 vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 8

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 9Thus, the required scalar components are –7 and 6 while the vector components are 

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 106. Find the sum of the vectors

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 11

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 127. Find the unit vector in the direction of the vector

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 13

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 14

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:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 15

9. For given vectors, NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 16and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 17, find the unit vector in the direction of the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 18

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 19

10. Find a vector in the direction of vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 20which has magnitude 8 units.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 21

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 22

11. Show that the vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 23are collinear.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 24

Therefore, the given vectors are collinear.

12. Find the direction cosines of the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 25

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 26

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:

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

Now,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 27

14. Show that the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 28is equally inclined to the axes OX, OY, and OZ.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 29

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 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 30 respectively, in the ration 2:1

(i) internally

(ii) externally

Solution:

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 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 31

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 32

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 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 33

17. Show that the points A, B and C with position vectors,NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 34NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 35respectively form the vertices of a right angled triangle.

Solution:

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

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 36

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

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 37

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 38

19. If NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 39are two collinear vectors, then which of the following are incorrect:

A. NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 40, for some scalar λ

B. NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 41

C. the respective components of NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 42are proportional

D. both the vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 43have same direction, but different magnitudes

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 44

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.2 - 45

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