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Class 12 RD Sharma chapter 22 exercise 22.7 solution is the best book which is available when it comes for the practice of mathematics for the class 12th CBSE students. Class 12th board exams are very important for every student. That's why RD Sharma class 12th exercise 22.7 has been recommended by great experts to grab each concept properly.

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Algebra of vectors exercise 22.7 question 1

Point A, B and C are collinear

Prove, that the position vectors are parallel to each other, so that they have one common point

Point A, B and C with position vectors respectively

Let O be the point of origin for the position vectors

Now, Position vector B – position vector A

…(i)

Position of vector C – Position of vector B

…(ii)

Substituting (i) in (ii)

Thus, are parallel vectors

As both vectors have one common point in B

are collinear

Thus, point A, B and C are collinear.

Algebra of vectors exercise 22.7 question 2(i)

Point A, B and C are collinear

Prove, that the position vectors are parallel to each other.

Point A, B and C with position vectors respectively

So, Position of B vector – Position of A vector

…(i)

Similarly find

Position of C vector – Position of B vector

…(ii)

Substituting (i) in (ii)

Thus,

So we say that parallel to each other.

Here B is a common point in both vector

Thus, point A, B and C are collinear.

Algebra of vectors exercise 22.7 question 2(ii)

Point A, B and C are collinear

Prove, that the position vectors are parallel to each other

Are non-coplanar vectors

Let, points A, B and C be the position vectors for respectively

Position vector B – Position vector A

…(i)

Similarly,

…(ii)

Substitute (i) in (ii)

Hence, are parallel vectors.

As B point is common in both vectors

Thus, A, B and C are collinear points.

Algera of vectors excercise 22.7 question 3

Point A, B and C are collinear

Obtain the parallel vectors and if any common points is there they are parallel to each other

Three vectors are given.

Let,

… (i)

Similarly

… (ii)

Put (i) in (ii)

Thus,

From above result, B is the common point in

A, B and C points are collinear.

Algera of vectors excercise 22.7 question 4

As the given vectors are collinear, then use formula

Three vectors are collinear.

Let,

So the above three points A, B and C represents three vectors collinear to each other

As, A,B and C are collinear, then there exists

Comparing

Put the value of

Algera of vectors excercise 22.7 question 5

Given position vectors are collinear for all the real values of

To be collinear, vectors must be a multiple of another.

Are non collinear vectors .

Let, position vectors of points X, Y and Z are respectively.

Then, Position of vector Y – Position of vector X

Similarly

Position of vector Z – Position of vector Y

… (i)

Now,

Position of vector X – Position of Z

…(ii)

From (i) and (ii)

Here point Z is common

Thus, we can say that for all real values of given position vectors are parallel.

Algebra of vectors exercise 22.7 question 6

A, B and C are collinear points

From the origin, point O towards a point ‘A’.

A, B and C are collinear

As per shown figure above

Where O must be the origin

We have,

From above figure we can say

Algebra of vectors exercise 22 .7 question 7

Given position vectors are collinear

Just prove that one vector can be represented in form of another

Let,

… (i)

(From (i))

Thus are collinear.

Algebra of vectors exercise 22.7 Question 8

Represent point in form of vectors and use

Points are collinear

If they are collinear then

Comparing

Put the value of

Algebra of vectors exercise 22.7 question 9

Given points are collinear

If the points are collinear then they are parallel.

Are collinear

Let,

Position of B – Position of A

… (i)

Position of C – Position of B

… (ii)

From (i) and (ii)

Thus are parallel to each and B being the common point

A, B and C are collinear

Thus, are collinear.

Algebra of vectors exercise 22.7 question 10

If one vector is scalar product of another vector, then they are parallel and collinear.

Are collinear

Comparing we get

… (i)

… (From (i))

Value of m is 9

Algebra of vectors exercise 22.7 question 11

When, in a three collinear points A, B and C, if B divides AC then formula is

Are collinear points

… (i)

… (ii)

Rewriting (i) and (ii)

… (iii)

… (iv)

From (iii)

Thus, are parallel to each other

Therefore they are collinear

Now,

Now, if B is dividing AC internally into m and n then,

Comparing,

… (v)

… (vi)

… (vii)

Now, solving equation (v) and (VI) by elimination method

If we suppose n=1 then

For all the three equation.

Algebra of vectors exercise 22.7 question 12

AB and CD intersect at the point P

If intersect at P, it makes A-P-B collinear and C-P-D collinear. So prove they are collinear

Position vector of P – Position vector of A

… (i)

Position vector of B – Position vector of P

cgfy… (ii)

Thus, A-P-B are collinear

Position vector of P – Position vector C

Position vector of D – Position vector of P

Thus, are collinear

If A-P-B are collinear and also C-P-D are collinear

Hence intersect at P

Algebra of vectors exercise 22.7 Question 13

Use the formula to prove it is collinear

Comparing

RD Sharma Class 12th Exercise 22.7 material is a good alternative for exam preparation as it follows the CBSE syllabus and covers all topics. The RD Sharma Class 12 solution of Algebra of Vectors exercise 22.7 contains 14 questions that help students get a good idea about the concept used.

Dot and cross product of two vectors

Unit vectors and position vector

Collinear vectors

Non-collinear vectors

Non-planar vectors

**The benefits of RD Sharma class 12th exercise 22.7 are:**

RD Sharma Class 12 Solutions Chapter 22 Exercise 22.7 material contains easy to understand Solutions for which the answers are given step-by-step. Students can refer to this material to ensure efficient preparation while saving time. It is comprehensive, detailed and follows the CBSE syllabus.

RD Sharma class 12th exercise 22.7 material is prepared by a group of subject experts who have years of experience with the question paper pattern. This is why students can rest assured that the material they are referring to has the best quality answers.

As RD Sharma class 12th chapter 22 exercise 22.7 material covers the entire syllabus there is a possibility that the questions from RD Sharma class 12th exercise 22.7 material can appear in exams as well. In order to prepare well for the board exams, students can use this material to get more knowledge on the subject.

RD Sharma class 12th exercise 22.7 material is available on Career360's website and is free to access. Students can access all the answers through any device with an internet connection. They can simply search the book name and exercise number on the website to get relevant results. RD Sharma class 12th exercise 22.7 is an easy and convenient alternative to textbooks.

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Download E-book**RD Sharma Chapter wise Solutions**

- 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 a vector?

A vector consists of both a magnitude and a direction.

2. What is a collinear vector?

Vectors are considered to be collinear vectors when it is said that two or more vectors lie on the same line segment.

3. Is it safe to download the RD Sharma solutions online?

Yes, it is entirely safe to download the solutions from Careers360 for trusted authenticated study material.

4. How many exercises do the Algebra of vectors chapter consist of?

12 exercises can be solved easily with the help of RD Sharma solutions in much less time.

5. Where can I find the latest version of RD Sharma Solutions class 12?

The Careers360 website provides all the updated copies of every class and chapter's RD Sharma solutions.

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