##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Lovekush kumar saini | Updated on Jan 25, 2022 11:55 AM IST

RD Sharma is a well-known name for many students in CBSE schools. Many schools widely use the RD Sharma class 12 solution of The plane exercise 28.8 for maths. Not only students, the RD Sharma class 12th exercise 28.8 is used by many teachers and experts to take in reference while giving lectures or preparing question papers. Class 12 RD Sharma chapter 28 exercise 28.7 solution is well known for its basic understanding and simple concepts which are very easy for beginners. RD Sharma solutions Their main motive is to encourage students to learn maths in the simplest possible way.

**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 **

The Plane exercise 28.8 question 1

We know that equation of a plane parallel to given plane (i) is

…(ii)

As given that, plane (ii) is passing through the point so it satisfy the plane (ii)

Put the value of k in equation (ii),

So, equation of the required plane is,

The Plane exercise 28.8 question 2

…(i)

We know that the equation of a plane parallel to given plane (i) is

… (ii)

As given that plane (ii) is passing through the point so it satisfy the equation (ii)

Put the value of k in equation (ii)

So, the equation of the required plane is

The Plane exercise 28.8 question 3

… (i)

As given that, plane (i) is passing through the point so it satisfy the equation (i)

Put the value of k in equation (i)

Multiplying by 6 we get

The Plane exercise 28.8 question 4

is given by

∴ The equation of the plane passing through the line of intersection of given two planes

and is given by

… (i)

As given that, plane (i) is passing through the point

Putting the value of k in equation (i)

So, the equation of required plane is

The Plane exercise 28.8 question 5

and is

…(i)

We know that, two planes are perpendicular if

…(ii)

Given, plane (i) is perpendicular to plane

…(iii)

Using (i) and (iii) in equation (ii)

Putting value of k in equation (i)

Multiplying with 14 we get

The Plane exercise 28.8 question 6

and is given by

… (i)

We know that, two planes are perpendicular if

… (ii)

Given, plane (i) is perpendicular to plane,

… (iii)

Using (i) and (iii) in equation (ii)

Putting the value of k in equation (iii)

Multiplying with 19 we get

The Plane exercise 28.8 question 7

and

… (i)

Equation (i) is passing through origin, so

Put the value of k in equation (i)

Multiplying by 3, we get

The Plane exercise 28.8 question 8

and is given by

… (i)

Plane (i) is passing the through the point so

Putting the value of k in equation (i)

Multiplying by -3

The Plane exercise 28.8 question 9

and

… (i)

Also this is perpendicular to the plane …(ii)

We know that, two planes are perpendicular if

∴ Putting this value of in equation (i) we get equation of plane as

The Plane exercise 28.8 question 10

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

The perpendicular distance from the origin is unity

Using equation (i) the required plane is

The Plane exercise 28.8 question 11

is given by

Plane

… (i)

Here the standard equation of plane is

Substituting the values in equation (i) we get

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

It is given that the plane is perpendicular to the plane

We know that where so we get

… (iii)

By comparing the standard equation in Cartesian form

Substituting these values in equation (iii)

On further calculation

Substituting the value of λ in equation (ii)

By taking LCM

We get

The Plane exercise 28.8 question 12

is given by

… (ii)

…(iii)

The plane in equation (iii) is perpendicular to the plane,

We know that, two planes are perpendicular if

Substituting in equation (iii), we obtain

… (iv)

This is vector equation of the required plane

Now

The Plane exercise 28.8 question 13

and Point

The family of planes is …(i)

Since it pass through

Vector equation is

The Plane exercise 28.8 question 14

given by

Is given by

So, equation of plane passing through the line of intersection of plane

is given by

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

Given that plane (1) is passing through

Put the value of k in equation (1)

Multiplying by ,we get

Equation of the required plane is

The Plane exercise 28.8 question 15

is given by

and is

, where …(i)

The plane passes through the point Therefore, this point will satisfy equation (1)

Substituting in equation (i), we obtain

The Plane exercise 28.8 question 16

…(i)

This plane is perpendicular to

We know that, two planes are perpendicular if

Equation of plane is

Vector form of plane is

Yes, line lies on the plane on satisfies

The Plane exercise 28.8 question 17

…(i)

Here, the position vector of this point is

∴ Equation (i) becomes

Substituting in equation (i), we obtain

… (ii)

This is vector equation of the required plane

Substituting in equation (ii)

The Plane exercise 28.8 question 18

- This plane doesn’t satisfies the given condition.
- The equation of the required plane is, .
- The equation of the required plane is,

and

and

, where k is some constant.

It is given that x-intercept of the required plane is twice its z intercept.

Either

When , the equation of the plane is

This plane does not satisfies the given condition, so this is rejected

When , the equation of the plane is

Thus, the equation of the required plane is .

Also, the equation of the plane passing through the point and parallel to the plane is

The Plane exercise 28.8 question 19

is given by

∴ Required equation of plane is for some λ

i.e.

According to question

Solving we get

Thus the equation of required plane is

The RD Sharma class 12th exercise 28.8 covers the chapter 'The Plane.' There are about 19 questions in this exercise that are extremely basic and simple to solve if you have knowledge of the fundamentals of this chapter. The RD Sharma class 12th exercise 28.8 covers all the essential concepts of this chapter that are mentioned below,

Equation of plane which is parallel to the line

Equation of plane passing through points and parallel to the plane

Equation of plane in scalar product form

Equation of plane passing through line of intersection of the planes

Mentioned below are some benefits of the RD Sharma class 12 solution chapter 28 exercise 28.8:-

The RD Sharma class 12th exercise 28.8 is used by teachers to take reference while teaching and also for preparing homeworks or question papers. Therefore, solving from the solution can help complete your homework on time and also easily.

You can trust the questions provided in the RD Sharma class 12 chapter 28 exercise 28.8 as it is generously prepared by experts of maths present in the country, so it gives you the best of knowledge about the concepts.

The RD Sharma solutions cover up the syllabus of NCERT and are updated yearly to correspond with the level of questions of NCERT so that students can also refer to the solutions to prepare for public exams.

The RD Sharma class 12th exercise 28.8 are available online for download on the Career360 website.

You don't need to pay any amount if you download the study material of RD Sharma if you download it from the Career360 website, it is available free of cost.

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. Who can use this material?

CBSE students who want to gain an insight on the subject and it’s core concepts can use this material.

2. How can I use this material?

Students can use this material as a guide for their exam preparation. They can also use it for completing their homework or assignments.

3. How are RD Sharma books better than NCERT?

RD Sharma books are much more comprehensive and detailed than NCERT books. They provide more information and hence are better than NCERT for Maths.

4. What is the cost of this material?

This material is available on Career360’s website for free.

5. Are there any hidden charges?

No, this material is absolutely free of cost and available to all on Career360’s website.

Application Date:05 September,2024 - 20 September,2024

Admit Card Date:13 September,2024 - 07 October,2024

Admit Card Date:13 September,2024 - 07 October,2024

Application Date:17 September,2024 - 30 September,2024

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

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! Trusted by 3,500+ universities globally

News and Notifications

Back to top