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The RD Sharma solutions are a common and best source for the practice of mathematics. The Class 12 RD Sharma chapter 22 exercise 22.6 solution deals with the complex chapter of Algebra of vectors that is quite tough for the students to solve, but the RD Sharma class 12th exercise 22.6 is an effective solution for all the problems. It is highly recommended by thousands of students and teachers for the self-guidance of the students.

Algebra of Vectors Exercise 22.6 Question 1

The magnitude of the vector is 7.

Hint:

Square and add using vector magnitude formula.

Given:

Solution:

Given:

We know that

Algebra of Vectors Exercise 22.6 Question 2

Answer:

The unit vector will be

Hint:

Use vector magnitude formula.

Given:

Solution:

Let the unit vector in the direction of

So, any unit vector in the direction of will be

So, the magnitude of the vector

So, the unit vector

Algebra of Vectors Exercise 22.6 Question 3

The unit vector will be

Hint:

Use vector magnitude formula.

Given:

Solution:

To find the resultant vector we add all the vectors by vector addition.

So, resultant vector is

So, the unit vector

Magnitude of vector

Algebra of Vectors Exercise 22.6 Question 4

The unit vector parallel to diagonals will be

Hint:

Use vector magnitude formula.

Given:

Solution:

Side BC parallel to:

So, resultant vector

So, vector

So, unit vector along the diagonal of parallelogram is

Similarly

Algebra of Vectors Exercise 22.6 Question 5

Hint:

Use vector magnitude formula

Given:

Solution:

We want to find the magnitude of vector

So,

If a vector is given by:

then the magnitude of vector is generally by which is equal to

Algebra of Vectors Exercise 22.6 Question 6

The position vector Q has co - ordinate

Hint:

Find the vector equation of Q.

Given:

and the co - ordinates of P is

Solution:

Let the position vector of point Q is

So, we need to find the value of

Position vector of Q – Position vector of P

So, the coordinates of position vector Q is

Algebra of Vectors Exercise 22.6 Question 7

Proved L H S = R H S

Hint:

Use vector magnitude formula for both L.H.S and R.H.S.

Given:

Solution:

In a right triangle , where CA is the hypotenuse.

BC is the perpendicular and AB is the base.

Vertices of triangle are given below

So,

Eq.(i)

Similarly,

Eq.(ii)

Eq.(iii)

So, three points form a right angle triangle.

Algebra of Vectors Exercise 22.6 question 8

Hint:

Use position vector formula.

Given:

Solution:

Let the position vector of the vertex A is

And similarly

Side AB is

Eq.(i)

Equation ( i ) vector representation of the side AB

Magnitude of side AB,

And similarly for side BC and CA

Eq.(ii)

Length of side BC and CA

Algebra of Vectors Exercise 22.6 question 9

Vector will be

Hint

Use position vector formula.

Given:

Vertices of the triangle are

Solution:

Centroid of the triangle with vertices and is given by:

In vector algebra, x is consider as a co – efficient of as a co – efficient of as a co – efficient of

So, the position vector of the centroid

So, the location of the centroid is

And the vector is,

Algebra of Vectors Exercise 22.6 question 10 (i)

Hint:

Use position vector formula.

Given:

in the ratio 2 : 1.

Solution:

A vector divides an line Internally as in

Position vector of P and Q are given as:

The position vector pf point R which divides the line joining two points P and Q internally in the ratio 2 : 1 is given by:

Algebra of Vectors Exercise 22.6 question 10 (ii)

Hint:

Use position vector formula.

Given:

i the ratio 2:1

Solution:

Position vector of P and Q are given as:

The position vector of point R which divides the line joining two points P and Q externally in the ratio 2 : 1 is given by:

A vector divides an line Internally as in m:n Externally

Algebra of Vectors Exercise 22.6 Question 11

Hint:

Mid – point of the vector joining the point

Given:

Two points are

Solution:

Let be the mid – point of the vector joining the point and

Then,

[ By mid – point formula ]

Algebra of Vectors Exercise 22.6 Question 12

Hint:

Unit vector

Given:

P and Q are the points

Solution:

Any unit vector on the direction of is

Required unit vector

Algebra of Vectors Exercise 22.6 Question 13

Hence proved

Hint:

Use distance formula

Given:

Solution:

Let BC length be a, AC length be b and AB length be c.

[ Use distance formula of two points ]

[ Use distance formula of two points ]

[ Use distance formula of two points ]

ABC is right angle triangle.

Algebra of Vectors Excercise 22.6 Question 14

Hint:

Mid – point

Given:

The points are

Solution:

Let R the mid - point of the line joining the point P and Q.

∴The mid – point are

Algebra of Vectors Excercise 22.6 Question 15

Answer:Hint:

Unit vector of

Given:

is a unit vector.

Solution:

Algebra of Vectors Exercise 22.6 Question 17

Answer:Hint:

Unit vector , new vector = unit vector of

Given:

Solution:

Let be the new vector

Algebra of Vectors Exercise 22.6 Question 18

Hint:

A vector having magnitude 1 and parallel to

Given:

Solution:

If is the resultant of

Now, a vector having magnitude 5 and parallel to

Algebra of Vectors Exercise 22.6 Question 19

units

Hint:

By triangle law of addition.

Given:

Solution:

[ By triangle law of addition ]

..as D is the midpoint of

[ By triangle law of addition ]

The RD Sharma class 12 solution of Algebra of vectors exercise 22.6 is an essential chapter to score good marks in the board exam. The RD Sharma class 12th exercise 22.6 consists of 20 questions that cover all the important concepts of the chapter that is mentioned below-

Magnitude of the vector

Unit vector

Addition and subtraction of vectors

Multiplication and division by a scalar quantity

Dot and Cross product

Position vector

Benefits of using the RD Sharma class 12 solution chapter 22 exercise 22.6 are:-

The RD Sharma solutions are used by thousands of students in the country as it has been proven to be a mindblowing study material for any type of student whether they like to solve maths or not.

The RD Sharma class 12th exercise 22.6 provides questions that are asked in the board exams, so a thorough practice of the RD Sharma solutions can result in scoring high marks.

The homeworks assigned by teachers is also taken from the RD Sharma class 12 chapter 22 exercise 22.6 as it is preferred by teachers as well when it comes to providing lectures and preparing question papers.

The RD Sharma solutions are always updated to the latest version, and it provides solved questions so that any students who face problems in solving questions from the NCERT they can refer to these solved questions for help.

The RD Sharma class 12th exercise 22.6 is available for download online on the website of Careers360, it provides all the study materials of RD Sharma online and also it is free of cost to download from the site.

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1. How many exercises do chapter 22 consist of?

Chapter 22 of RD Sharma consists of 5 exercises that cover up all the essential concepts of the chapter.

2. Is it helpful for the preparation for the board exam?

Yes, any student who is to appear for the board exams should go through these solutions for better results.

3. From where can I download the PDF and study material?

You can download the free PDF for RD Sharma solutions from the official website of Careers360 free of cost.

4. How much is the cost of the RD Sharma class 12 solutions chapter 22 exercise 22.6?

The online PDFs are free of cost and can be downloaded through any device from the website of Careers360.

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

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

Mar 22, 2023

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