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Edited By Lovekush kumar saini | Updated on Jan 27, 2022 05:03 PM IST

The practice sessions for the class 12 students go unending until their exams. Therefore, the students must make sure that they are using a proper solution book for their reference. The solutions for mathematical sums can be derived using various methods; it is in the hands of the teachers to make the students aware of the right method. When students struggle to solve the sums in the Scalar and Dot Product portion, they can use the RD Sharma Class 12th Chapter 23 MCQ book for clarification.

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Scaler and dot product exercise multiple choice question 1

Option (c)

Apply Elimination method to find , then find

satisfy the equation and

Where, and is the angle between

____________

Put in equation (i)

Now,

Hence, option (c) is correct

Scaler and dot product exercise multiple choice question 2

Option (b)

You must know about the concept of dot product

............(i)

Putting in (i)

...........(ii)

Put in (ii)

Hence, option (b) is correct

Scaler and dot product exercise multiple choice question 3

Option (d)

You must know the formula of

Squaring on both sides,

Now,

Hence, option (d) is correct

Scaler and dot product exercise multiple choice question 4

Option (c) write what is given in option c from book pdf

If are unit vectors then

are two unit vectors and is an angle between them

According to the given question,

Squaring both side, we get

As both are unit vectors

Scaler and dot product exercise multiple choice question 5

Magnitude of a vector

Magnitude of a vector

Hence, it is unit vector

Scaler and dot product exercise multiple choice question 6

Option (c)

Let be the origin

We know that unit vector along

Therefore, angle between

Hence, option (c) is correct

Scaler and dot product exercise multiple choice question 7

are unit vector

are unit vector

We know that,

So cannot be greater than one.

Hence, option (a) is correct

Scaler and dot product exercise multiple choice question 8

Option (b) an ellipse

You must know the value of , when are perpendicular

are perpendicular, locus

If vectors are perpendicular, then

This is the equation of ellipse

Hence, option (b) is correct

Scaler and dot product exercise multiple choice question 9

Option (b)

You must know the formula of perpendicular to

Vector component of perpendicular to

Vector is perpendicular to

Hence, option (b) is correct

Scaler and dot product exercise multiple choice question 10

Option (c)

Use the formula

and angle between

Here

First we have to find both diagonals

Length of the two diagonal will be

And again

Hence length of the longest diagonal

Scaler and dot product exercise multiple choice question 11

Option (d)

Use the concept of unit vector,

is a non-zero vector, and is a non-zero scalar and is a unit vector

is a unit vector

Hence, option (d) is correct

Scaler and dot product exercise multiple choice question 12

Option (b)

You must know the formula of and range of

is the angle between

Hence, option (b) is correct

Scaler and dot product exercise multiple choice question 13

Option (b)

Use the formula of finding the angle between two vectors

angle between them is obtuse and angle between and is acute and less than

Let be the angle between

Since, is obtuse angle

Hence, option (b) is correct

Scaler and dot product exercise multiple choice question 14

Option (c)

Use the formula of

are mutually perpendicular and

are mutually perpendicular.

Now,

Hence, option (c) is correct

Scaler and dot product exercise multiple choice question 15

Option (c) 14

If are perpendicular, then

are perpendicular.

Let

If are perpendicular, then

Hence option (c) is correct.

Scaler and dot product exercise multiple choice question 16

Option (a) 1

The projection of

Projection of the vector along the vector

The projection of

Hence, option (a) is correct.

Scaler and dot product exercise multiple choice question 17

Option (b)

Use the formula of , when are perpendicular

are perpendicular

Given that,

are perpendicular

For option (a),

Hence, option (a) is not correct

For option (b),

Hence, option (b) is correct.

Scaler and dot product exercise multiple choice question 18

Option (c) 0

Use the identity

Hence, option (c) is correct.

Scaler and dot product exercise multiple choice question 19

Option (a)

Use the identity

are unit vectors inclined at an angle

Now,

Hence, option (a) is correct.

Scaler and dot product exercise multiple choice question 20

Option (c) 4

Magnitude of a vector

are unit vectors and the greatest value of

Now,

Hence, maximum value of

So, option (C) is correct.

Scaler and dot product exercise multiple choice question 21

Option (c)

You must know the formula for finding angle between two vectors

, angle between them is acute.

Angle between the vectors is acute

Hence, option (c) is correct.

Scaler and dot product exercise Multiple choice question 22

Option (d)

You must know the formula of magnitude of vector

are unit vectors inclined at an angle such that

We know is always lies between

Hence, option (d) is correct.

Scaler and dot product exercise multiple choice question 23

Option (d)

Use the identity

is perpendicular to and makes angle and with and respectively

Hence, option (d) is correct.

Scaler and dot product exercise multiple choice question 24

Option (b)

You must know the concept of orthogonal projection

Orthogonal projection of on

Orthogonal projection of on

Hence, option (b) is correct.

Scaler and dot product exercise multiple choice question 25

Option (d)

Vector a and b are perpendicular if their dot product is zero.

is an acute angle

are perpendicular

Both are perpendicular to each other

Scaler and dot product exercise multiple choice question 26

Option (b)

You must know the formula to find angle between two vectors

Hence, option (b) is correct.

Scaler and dot product exercise multiple choice question 27

Answer:Option (c)

Hint:

You must know the formula of

Given:

Solution:

We know that,

Hence, option (c) is correct

Scaler and dot product exercise multiple choice question 28

Option (c)

Apply the identity

We know that,

Scaler and dot product exercise multiple choice question 29

Option (a)

You must know the identity

to be a unit vector

According to the given question,

Scaler and dot product exercise multiple choice question 30

Option (c)

Use the formula of projection

Projection of is zero

Hence, option (c) is correct

The syllabus of chapter 23 in the class 12 mathematics book is very thought-provoking and requires the concentration of the students to solve it quickly. This chapter has a couple of exercises, ex 23.1 and ex 23.2. The Multiple Choice Questions (MCQ) part contains 30 questions in the textbook. It covers the concepts like the projection of vectors, position vectors, angle between two vectors, and so on. It is not enough when the students know only the right answer among the choices; they must know how to solve each question quickly to find the right option. This is where the Class 12 RD Sharma Chapter 23 MCQ Solution helps the student in the right way.

They must grasp the formula to be applied as soon as they look into the question; this requires a lot of practice. The additional practice questions given in the RD Sharma Class 12th Chapter 23 MCQ book will make the students sharpen their knowledge in the particular concept. Many CBSE school students follow the RD Sharma Class 12th Chapter 23 MCQ reference book updated according to the recent NCERT syllabus. This has made the RD Sharma books the most recommended ones among the school students.

Solving MCQs should not take much time; tricks and shortcuts are essential to solve the sums and score more marks easily during the examination. In addition to helping in these circumstances, the RD Sharma Chapter 23 MCQ Solution book also provides various other benefits. RD Sharma Solutions in the first place, it is available completely free of cost at the Career 360 website. This makes the RD Sharma Class 12 Solutions Scalar and Dot Product Chapter 23 MCQ reference book a go-to option for most school students.

As the staffs prepare their questionnaires using the sums picked from the RD Sharma Class 12 Solutions Chapter 23 MCQ, the students who prepare with this book have a greater advantage. Once you start using the RD Sharma books for your exam preparation, no one can stop you from crossing your benchmark scores.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Why are RD Sharma books the better option to use for homework completion?

The students understand the mathematical concepts mostly by doing their homework. When a good solution guide clarifies the doubts, it will be easy for them to prepare for their examinations.

2. Which reference book can I use to get hints regarding class 12, chapter 23 MCQ?

The RD Sharma Class 12th Chapter 23 MCQ reference book can be used to clarify any doubts regarding the Multiple Choice Questions of chapter 23.

3. Where is the RD Sharma reference guide available for free access?

The Career 360 website provides free access to all its visitors to view the RD Sharma solution guides.

4. What makes the RD Sharma bookstand from the rest of the reference guides available in the market?

The solved sums in the RD Sharma books are provided by the mathematical experts. Many teachers use this book to frame questions papers for tests and exams. And there are many more advantages of using this set of solution books.

5. How many questions are answered for the Chapter 23 MCQ in the RD Sharma solution guide?

The Chapter 23 MCQ part contains around 30 questions. The right answers are given for each of these questions and additional practice questions in the RD Sharma Class 12th Chapter 23 MCQ book.

Sep 11, 2024

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