# RD SHARMA Solutions for Class 12-science Maths Chapter 23 - Algebra of Vectors

Page / Exercise

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.1

Question 1(i)

Represent graphically a dispacement of 40 km, 30° east of north.

Solution 1(i)

Question 1(ii)

Represent graphically a displacement of 50 km, south-east

Solution 1(ii)

Here, vector  represents the displacement of 50 km, south-east.

Question 1(iii)

Represent graphically a displacement of 70 km, 40° north of west.

Solution 1(iii)

Here, vector  represents the displacement of 70 km, 40° north of west.

Question 2

Classify the following measures as scalars and vectors.

(i) 15 kg

(ii) 20 kg weight

(iii) 45°

(iv) 10 metres south-east

(v) 50 m/s2

Solution 2

(i) 15 kg is a scalar quantity because it involves only

(ii) 20 kg weight is a vector quantity as it involves both magnitude and direction.

(iii) 45° is a scalar quantity as it involves only magnitude.

(iv) 10 metres south-east is a vector quantity as it involve direction.

(v) 50 m/s2 is a scalar quantity as it involves magnitude of acceleration.

Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5

Question 1

Solution 1
Question 2

Solution 2

Question 3

Solution 3
Question 4
Solution 4
Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.3

Question 1

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors

Solution 1

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.4

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.

Solution 6

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.5

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Find |AB| in each case.

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 12

Solution 12

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.7

Question 1

Solution 1

Question 2 (i)

Solution 2 (i)

Question 2 (ii)

Solution 2 (ii)

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Using vectors, find the value of λ such that the points

, - 10, 3), (1 -1, 3) and (3, 5, 3) are collinear.

Solution 13

Question 1

Solution 1

Question 2 (i)

Solution 2 (i)

Question 2 (ii)

Solution 2 (ii)

Question 2 (iii)

Solution 2 (iii)

Question 2 (iv)

Solution 2 (iv)

Question 3 (i)

Solution 3 (i)

Question 3 (ii)

Solution 3 (ii)

Question 4

Solution 4

Question 5 (i)

Solution 5 (i)

Question 5 (ii)

Solution 5 (ii)

Question 6 (i)

Solution 6 (i)

Question 6 (ii)

Solution 6 (ii)

Question 7 (i)

Solution 7 (i)

Question 7 (ii)

Solution 7 (ii)

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

## Chapter 23 - Algebra of Vectors Exercise Ex. 23.9

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7 (i)

Solution 7 (i)

Question 7 (ii)

Solution 7 (ii)

Question 7 (iii)

Solution 7 (iii)

Question 8

Solution 8

Question 9

Solution 9

Question 10

If a unit vector  makes and angles  and an acute angle θ with , then find θ and hence, the components of .

Solution 10

Question 11

Solution 11

Question 12

Solution 12

## Chapter 23 - Algebra of Vectors Exercise MCQ

Question 1

If in a Δ ABC, A = (0, 0), B = (3, 3), = (-3, 3), then the vector of magnitude 2 units directed along AO, where O is the circumcentre of Δ ABC is

Solution 1

Correct option:(a)

Question 2

Solution 2

Correct option:(c)

Question 3

1. C is a mid-point of AB
2. C divides AB in the ratio 2:1
3. 3 AC = 5CB
4. 2 AC = 3CB

Solution 3

Correct option: (c)

Question 4

Solution 4

Correct option: (d)

Question 5

1. 40
2. -40
3. 20
4. -20
Solution 5

Correct option: (b)

Question 6

Solution 6

Correct option: (b)

Question 7

1. Null vector
2. Unit vector
3. Constant vector
4. None of these
Solution 7

Correct option: (b)

Question 8

Solution 8

Correct option: (c)

Question 9

Solution 9

Correct option: (b)

Question 10

Solution 10

Correct option: (b)

Question 11

1. Rhombus
2. Rectangle
3. Square
4. Parallelogram
Solution 11

Correct option: (d)

Question 12

Solution 12

Correct option: (a)

NOTE: Answer not matching with back answer.

Question 13

Solution 13

Correct option: (d)

Question 14

1. form an isosceles triangle
2. form a right triangle
3. are collinear
4. form a scalene triangle
Solution 14

Correct option: (a)

Question 15

1. (2,-3)
2. (-2,3)
3. (-2,-3)
4. (2,3)
Solution 15

Correct option: (a)

Question 16

Solution 16

Correct option: (c)

Question 17

Solution 17

Correct option: (d)

Question 18

If a and b are two collinear vectors, then which of the following are incorrect?

Solution 18

Correct option: (d)

Question 19

In Figure 23.67, which of the following is not true?

Solution 19

Correct option: (c)

## Chapter 23 - Algebra of Vectors Exercise Ex. 23VSAQ

Question 1

Solution 1

Question 2

Solution 2

Question 3

Define position vector of a point.

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

If  are position vectors of the points A, B and C respectively, write the value of

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

Question 27

Solution 27

Question 28

Solution 28

Question 29

Solution 29

Question 30

Solution 30

Question 31

Solution 31

Question 32

Solution 32

Question 33

Solution 33

Question 34

Solution 34

Question 35

Solution 35

Question 36

Solution 36

Question 37

Solution 37

Question 38

Solution 38

Question 39

Solution 39

Question 40

Solution 40

Question 41

Solution 41

Question 42

Solution 42

Question 43

Solution 43

Question 44

Solution 44

Question 45

Solution 45

Question 46

Solution 46

Question 47

Solution 47

Question 48

Solution 48

Question 49

Solution 49

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