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Edited By Lovekush kumar saini | Updated on Jan 25, 2022 11:54 AM IST

The RD Sharma solutions are a country-wide famous series of books for its extraordinary concepts that are so basic for students to understand. The Class 12 RD Sharma chapter 28 exercise 28.5 solution contains the questions for the chapter ‘The Plane’, which is also explained theoretically in a very simple language for any student to understand. The RD Sharma class 12th exercise 28.5 is the best study material to make your concept clear in this chapter.

The required vector equation of plane is

Using

Vector equation of the plane passing through the points (1,1,1), (1,-1,1) and (-7,-3,-5)

Let A (1,1,1), (1,-1,1) and (-7,-3,-5) be the coordinates.

The required plane passes through the point A (1, 1, 1) whose vector is

and is normal to the vector given by

clearly.

The vector equation of required plane is: -

The Plane exercise 28.5 question 2

The vector equation of required plane is

Using formula

Vector equation of plane passing through the points P(2, 5, -3), Q(-2, -3, 5) and R(5, 3,-3)

The required plane passes through the point (2, 5, - 3) whose position vector is

and is normal to the vector given by

The vector equation of the required plane is

The Plane exercise 28.5 question 3

The required vector equation of plane is:

Vector equation of the plane passing through the point A (a, 0, 0), B (0, b, 0) and

C (0, 0, c). Prove that

The required plane passing through the point A (a, 0, 0) whose position vector is

and is normal to the vector given by

The vector equation of required plane is

For reducing (i) to normal form, we need to divide both sides of (i) by

Then, we get

Therefore, the normal form of plane (i) is

So, the distance of plane (i) from the origin

Hence proved

The Plane exercise 28.5 question 4

The required vector equation of plane is a(x - 1) + b(y - 1) + c (z + 1)=0,

Where 5a + 3b - 4c = 0

Convert to the vector form by the given points.

Let A (1, 1, -1), B (6, 4, -5) and C (-4, -2, 3)

The required plane passes through the point A (1, 1, -1) whose vector is

and is normal to the vector given by

So, the given points are collinear.

Thus, there will be an infinite number of planes passing through these points.

Their equations passing through (1, 1, -1) are given by

a(x - 1) + b(y - 1) + c (z + 1)=0 .....(i)

Since this passes through B (6, 4, -5)

a(6 - 1) + b(4 - 1) + c (-5 + 1)=0

5a + 3b - 4c = 0 .....(ii)

From (i) and (ii) the equations of the infinite planes are

a(x - 1) + b(y - 1) + c (z + 1)=0,

Where 5a + 3b - 4c = 0

The Plane exercise 28.5 question 5

The required vector equation of plane is 9x + 2y - 7z - 15 = 0

Using

Co-ordinates of the given plane are A (3, 4, 2), B (2, -2, -1) and C (7, 0, 6)

General equation of plane is given by-

Again putting point C in general equation

Let’s cross multiply;

Substituting a, b and c by their values in equation (i)

Divide by λ

Also See:

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.1

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.2

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.3

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.4

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.6

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.7

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.8

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.9

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.10

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.11

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.12

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.13

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.14

RD Sharma Solutions Class 12 mathematics chapter 28 exercise 28.15

RD Sharma Solutions Class 12 mathematics chapter 28 exercise MCQ

RD Sharma Solutions Class 12 mathematics chapter 28 exercise FBQ

RD Sharma Solutions Class 12 mathematics chapter 28 exercise VSA

The RD Sharma class 12th exercise 28.5 deals with the chapter The plane, which is a flat, 2-dimensional surface with infinite dimensions but zero thickness. The RD Sharma class 12 solution of The plane exercise 28.5 consists of a total of 5 questions that cover up all the essential concepts of the chapter like the equation of a plane, equation of the plane passing through points, equation of line under planes condition, equation of the plane passing through three points and Vector equation of plane.

Listed below are few reasons that explains the benefits of the RD Sharma class 12 solution chapter 28 exercise 28.5 :-

The RD Sharma class 12th exercise 28.5 are best solutions to refer to when you are solving your NCERT questions as it contains all the possible solutions.

The solutions are updated according to the NCERT, so if you face any problem while problem solving the solutions are present for your help.

The RD Sharma class 12 chapter 28 exercise 28.5 is trusted by thousands of students from across the country, as any student who has preferred the RD Sharma solutions over other books have definitely seen positive results.

If you face any trouble while solving the exercise questions you can always refer to the solved questions given in the RD Sharma class 12th exercise 28.5 for understanding the concept.

The RD Sharma solutions are available for every student for free of cost on the Career360 website.

You just have to make one click on the Career360 website and in one second the online PDF will be downloaded on your device.

**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. Is the RD Sharma solution helpful for 11th std students?

Yes it is helpful for every student who is in class 11th or class 12th for their self-practice.

2. Is it helpful for self-practice?

It can be a guide for the students who like to self-test themselves on their recent lessons and then they can evaluate their performance based on their test.

3. Can I take help from the RD Sharma solution for solving homework?

Yes, you can take in reference to the solution as teachers assign homework from these solutions only .

4. Is the RD Sharma solution updated every year?

Yes, these solutions are regularly updated so that it can match with the syllabus of the NCERT.

5. From where can I download the RD Sharma solution?

You can download the online PDFs from the Career360 website that are also free of cost.

Mar 22, 2023

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