##### Tallentex 2025 - ALLEN's Talent Encouragement Exam

ApplyRegister for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Edited By Satyajeet Kumar | Updated on Jan 24, 2022 06:20 PM IST

The RD Sharma solution chapters are said to be of the highest quality when it comes under the consideration of practicing maths with effective results from students all across the country. The Class 12 RD Sharma chapter 22 exercise MCQ solution are the multiple-choice questions, where each question has four options to choose from, thus making it easy for the students to confidently answer the questions. The RD Sharma class 12th exercise MCQ contains questions covering the basics and the tough level questions, all in the same solution paper.

**JEE Main 2025: Sample Papers | Mock Tests | PYQs | Study Plan 100 Days**

**JEE Main 2025: Maths Formulas | Study Materials**

**JEE Main 2025: Syllabus | Preparation Guide | High Scoring Topics **

Algebra of Vectors exercise Multiple choice question 1

Hint: You have to find circumcenter of

Given: In , magnitude

Solution:

Let Positive vector of be

...................(1)

......................(2)

Substituting from (2) and (1) we get

The positive vector of O is

Algebra of Vectors exercise Multiple choice question 2

Answer:Hint:

Given: If are vector forming consecutive side of rectangular Hexagon the vector representing side is

Solution: Let be rectangular Hexagon such that

We know

is parallel such that

In , we know

In , we have

Algebra of Vectors exercise Multiple choice question 3

Answer:Hint:

Given: Forces act along and . If resultant pass through on then

Solution: Draw the perpendicular to line

Let i be unit actor along

The Resultant Force ……….. (1)

The angle between and force

we know that

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

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

On adding (i) and (ii)

Algebra of Vectors exercise Multiple choice question 4

Answer: None of theseHint: Find

Given: If are three non-vectors no two of which are collinear and vector is collinear with is collinear with then

Solution: Let …………. (1)

…………. (2)

Then

Multiply equation (2) by 2

...............(3)

Subtract equation (3) by eq (1)

Comparing both sides

Algebra of Vectors exercise Multiple choice question 5

Answer:Hint: Find a

Given: If are collinear then equal to

Solution:

Now find and

Take cross product

Algebra of Vectors exercise Multiple choice question 6

Hint: Find

Given: If is intersection of diagonal of parallelogram. and is any point that

Solution: Let consider the point as origin is the midpoint of

................(1)

Also is midpoint of

On add (1) and (2)

Algebra of Vectors exercise Multiple choice question 7

Answer: Unit vectorHint: is which vector

Given: The vector

Solution:

Algebra of Vectors exercise Multiple choice question 8

Hint: Find

Given: In regular Hexagon then

Solution: We have

In we have

In we have

Algebra of Vectors exercise Multiple choice question 9

Answer:Hint: Find plane of vector equation

Given: The vector equation of plane passing through provide that

Solution: ................(1)

..............(2)

By comparing (1) and (2)

Algebra of Vectors exercise Multiple choice question 10

Answer:Hint:

Given : If and are circumcenter and orthocenter of , then

Solution: According to properties of triangle circumcenter in the sum of distance from circumcentre to orthocentre

Algebra of Vectors exercise Multiple choice question 11

Answer: ParallelogramHint: Find

Given: If are position vectors of points and such that no three of them are collinear then is

Solution: Given

Since

So position vector midpoint of position vector of midpoint of

Hence bisect each other

The given point is parallelogram.

Algebra of Vectors exercise Multiple choice question 12

Hint: Find the centroid

Given: Let G is centroid of then bisector in terms of

Solution: Take as origin them position vector are given and respectively

The centroid

Algebra of Vectors exercise Multiple choice question 13

Answer:Hint: Find equals - ?

Given: If is regular Hexagon then

Answer: We have

Algebra of Vectors exercise Multiple choice question 14

Answer: Form as isosceles triangle.Hint: for which triangle

Given: The position vector of points and are

Solution:

Hence

It forms isosceles triangle.

Algebra of Vectors exercise Multiple choice question 15

Answer:Hint: value find

Given: If three points have position vectors respective are collinear , then

Solution: If

Since vectors are collinear.

...................(1)

....................(2)

Substitute in (1) and (2)

Algebra of Vectors exercise Multiple choice question 16

Answer:Hint:

Given: is parallelogram with and as diagonal

Solution: is parallelogram So

(Subtraction theorem)

(Subtraction theorem)

=

Algebra of Vectors exercise Multiple choice question 17

Answer:Hint:

Given: If is parallelogram

Solution:

Algebra of Vectors exercise Multiple choice question 18

Answer: Both have same direction but different magnitudeHint: Talk about

Given: If are collinear vector, then which of the following are incorrect?

Solution: If are two collinear vectors then they are parallel

Therefore,

Thus, respective component of proportional. However, vector have different direction.

So Statement is incorrect

That both have same direction but different magnitude.

Algebra of Vectors exercise Multiple choice question 19

Answer:Hint: According to diagram

Given: Which of the following is not true?

Solution:

Hence, is not true.

Algebra of Vectors exercise Multiple choice question 20

Answer:Hint: Measure by

Given: The position vector of point which divide the join of point with position in ratio is:

Solution: Apply section formula the position vector require point

Since position vector of point divide line segment joining the point and where position vector are in ration

Algebra of Vectors exercise Multiple choice question 21

Answer:Hint: Initial vector find

Given: The vector with initial point terminal point is

Solution: Require vector

Algebra of Vectors exercise Multiple choice question 22

Answer:Hint: The length of median by median formula

Given: The vector represent two side . Find length of median,

Solution:

Algebra of Vectors exercise Multiple choice question 23

Answer:Hint: Find interval of

Given: If then lies in

Solution:

Algebra of Vectors exercise Multiple choice question 25

Hint: According to ratio

Given: The position vector of point which divide the join of points in ratio

Solution: Position vector

Since point vector are joint by divide line segment join and whose positive vector in ratio given

Algebra of Vectors exercise Multiple choice question 26

Answer:Hint:

Given: is rhombus whose diagonal intersect E then equal

Solution: Since in rhombus diagonal bisects each other,

But since they are opposite to each other they are opposite signs

...................(1)

...................(2)

Algebra of Vectors exercise Multiple choice question 27

Answer:Hint:

Given: If are position vectors of point

Then is equal to

Solution:

Magnitude:

The RD Sharma class 12 solution of Algebra of vectors exercise MCQ consists of a total of 27 questions, all covering the essential concepts of the chapter and you have to choose the correct option among all the options given in the question. RD Sharma solutions The RD Sharma class 12th exercise MCQ covers the below-given concepts of the Algebra of vectors chapter-

Scalar and Vector product

Addition and subtraction of vectors

Multiplication and division by a scalar quantity

Collinear and non-collinear

Unit vectors and position vector

The benefits that accrue by using the RD Sharma class 12 solution chapter 22 exercise MCQ are listed below-

The RD Sharma class 12th exercise MCQ can easily be accessed by downloading it from the official website of careers360 And any student can reach the solutions by sitting at home.

The RD Sharma class 12 chapter 22 exercise MCQ is the multiple choice question where students are provided with four options to choose from the given section which automatically makes their burden less.

The RD Sharma class 12th exercise MCQ is prepared by a group of people who have the expertise in this department and present you with the best of questions that have the probability of being asked in the board exams.

The solutions that you download from the Careers360 website doesn't ask you to pay any amount for the online PDFs and study materials, so it comes free of cost.

The RD Sharma class 12th exercise MCQ can also be used for solving homework as most of the teachers refer to these solutions while providing homework.

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download E-book- 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. What is the magnitude of a vector?

The magnitude of a Vector is the distance between the initial point P and the endpoint Q.

2. What is scalar in vector algebra?

A scalar is an element of a field that is used to define a vector space. A quantity described by multiple scalars, such as having both directions and magnitude, is called a vector.

3. What is the vector B formula?

Vectors A and B are said to be equal if lAl = lBl as well as their directions are said to be the same.

4. What are the types of vectors?

There are a few vectors mainly, zero vector, unit vector, position vector, co-initial vector, like and unlike vectors, coplanar vector, collinear vector, equal vector..

5. Can I take the help of the RD Sharma solution to solve homework?

Yes, as teachers refer to these solutions for assigning homework, it is helpful and less time-consuming.

Get answers from students and experts

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top