# RD Sharma Solution CLass 12 Mathematics Chapter 24 Scalar or Dot Product

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
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
Question 50
Solution 50
Question 51
Solution 51
Question 52

Solution 52

Question 53

Solution 53

Question 54

Solution 54

Question 55

Solution 55

Question 56

Solution 56

Question 57

Solution 57

Question 58

Solution 58

Question 59

Solution 59

Question 60

Solution 60

Question 61

Solution 61

## Chapter 24 – Scalar Or Dot Product Exercise Ex. 24.2

Question 1

Solution 1

Question 2

Prove that: If the diagonals of a quadrilateral bisect
each other at right angles, then it is a rhombus.

Solution 2

Question 3

(Pythagoras’s Theorem) Prove by vector method that in a
right angled triangle, the square of the hypotenuse is equal to the sum of
the squares of the other rum sides.

Solution 3

Question 4

Prove by vector method that the sum of the squares of
the diagonals of a parallelogram is equal to the sum of the squares of its
sides.

Solution 4

Question 5

Prove using vectors: The quadrilateral obtained by
joining mid-points of adjacent sides of a rectangle is a rhombus.

Solution 5

Question 6

Prove that the diagonals of a rhombus are perpendicular
bisectors of each other.

Solution 6

Question 7

Prove that the diagonals of a rectangle are
perpendicular if and only if the rectangle is a square.

Solution 7

Question 8

If AD is the median of
D ABC, using vectors, prove that

AB2 + AC2
CD2).

Solution 8

Question 9

If the median to the base of a triangle is
perpendicular to the base, then triangle is isosceles.

Solution 9

Question 10

In a quadrilateral ABCD, prove that AB2 + BC2
+
CD2+ DA2 = AC2 + BD2
+
4 PQ2, where P and Q are
middle points of diagonals
AC and BD.

Solution 10

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

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

## Chapter 24 – Scalar Or Dot Product Exercise MCQ

Question 1

Solution 1

Correct option: (c)

Question 2

Solution 2

Correct option: (b)

Question 3

Solution 3

Correct option: (d)

Question 4

Solution 4

Correct option: (c)

Question 5

(a) Null vector

(b) Unit vector

(c) Constant vector

(d) None of these

Solution 5

Correct option: (b)

Question 6

Solution 6

Correct option: (c)

Question 7

Solution 7

Correct option: (a)

Question 8

1. A circle
2. An ellipse
3. A hyperbola
4. None of these

Solution 8

Correct option: (b)

Question 9

Solution 9

Correct option: (b)

Question 10

Solution 10

Correct option: (c)

Question 11

Solution 11

Correct option: (d)

Question 12

Solution 12

Correct option: (b)

Question 13

Solution 13

Correct option: (b)

Question 14

Solution 14

Correct option: (c)

Question 15

Solution 15

Correct option: (c)

Question 16

1. 1
2. 0
3. 2
4. -1
5. -2
Solution 16

Correct option: (a)

Question 17

Solution 17

Correct option: (b)

Question 18

1. Positive
2. Negative
3. 0
4. None of these
Solution 18

Correct option: (c)

Question 19

Solution 19

Correct option: (a)

Question 20

Solution 20

Correct option: (c)

Question 21

1. (-4,7)
2. [-4,7]
3. R – [-4,7]
4. R – (4,7)
Solution 21

Correct option: (c)

Question 22

Solution 22

Correct option: (d)

Question 23

Solution 23

Correct option: (d)

Question 24

Solution 24

Correct option: (b)

Question 25

Solution 25

Correct option: (d)

Question 26

Solution 26

Correct option: (d)

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