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

Students of class 12 have a very vast syllabus when it comes to the subject of mathematics. Chapters like ‘The Plane’ are complex maths topics that make solving the problem challenging for students; that is why students are highly recommended to use the Class 12 RD Sharma chapter 28 exercise 28.7 solution to practice at home and improve their performance on the subject. The RD Sharma class 12th exercise 28.7 of The Plane of class 12 deals with various topics like,

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Equation of plane

Cartesian form of the equation of the plane

Vector Equation of planes in scalar product form

Vector Equation of planes in nonparametric form

The Plane exercise 28.7 question 1(i)

Required equation is

Using scalar form

We know that

represent a plane passing through a point having position vector and parallel to the vector and

Clearly,

Now the plane is perpendicular to X

Hence

We know that vector equation of plane in scale product form is given by

(a)

Put and in equation (a) we get

Hence the require equation is

The Plane exercise 28.7 question 1(ii)

Required vector equation is

Using scalar form

We know that the equation

represent a plane passing through a point whose position vector

Here

Normal vector

The vector equation of plane is in scalar product form in

Is the required vector equation

The Plane exercise 28.7 question 1(iii)

Using scalar form

We know that the equation

represents a plane passing through a point whose vector is and parallel to the vector and

Here

Normal vector

The vector equation of the plane in scalar product form is

The Plane exercise 28.7 question 1(iv)

Required vector equation is

We know that the equation

represents a plane passing through a point having position parallel to the vectors and

Clearly

Now the plane is perpendicular to X

Hence

We know that vector equation of plane in scalar product form is given as

Put and in equation (a) we get

Hence the required equation is

The Plane exercise 28.7 question 2(i)

Required Cartesian equation is

The plane is perpendicular to

We know that the equation

represents a plane passing through a point having position parallel to the vectors and

Here

The given plane is perpendicular to X

Vector equation of the plane in scalar product form is

Now put

So, we have

Divide by -3, we get

Hence the required equation is

The Plane exercise 28.7 question 2(ii)

Required Cartesian equation is 2y - z = 1

Using the equation of the plane

Since from the given equation

We know that the vector equation of a plane is scalar product form is given as

Substituting the value of and in equation (1)

We get

Now put

So we have

Hence the required equation of the plane is

The Plane exercise 28.7 question 3(i)

The required equation is

The plane is perpendicular to X so we find

Here

We know that the equation

represents a plane passing through a point having position and parallel to the vectors and

Clearly

Now the plane is perpendicular to

Hence

We know that the vector equation of plane in scalar product form is given by

Hence the required equation is

The Plane exercise 28.7 question 3(ii)

The required equation is

The plane is perpendicular to so we find

We know that represents

A plane passing through a point having position vector and parallel to the vectors and

Clearly

Hence

We know that vector equation of a plane in scalar product is given as

Hence the require equation is

Students can effectively start practicing RD Sharma class 12th exercise 28.7 of chapter 28 to get a hold on the concept to make it an asset while solving the questions. The RD Sharma class 12 solution of The Plane exercise 28.7 explains the equation of the plane among various logics and consists of a total of 8 questions.

Let's have a look at some of the benefits of using the RD Sharma class 12th exercise 28.7 mentioned below:-

The RD Sharma class 12 chapter 28 exercise 28.7 is used by teachers for conducting lectures and use an example to solve queries.

The questions assigned by the teachers for homework are also taken from the RD Sharma class 12th exercise 28.7 solution, therefore referring to the solution can help solve homework easily.

Most importantly, the questions are prepared by experts from across the country hence it is trusted by students and teachers as well that is why they use the questions from the solution to prepare question papers.

The RD Sharma class 12th exercise 28.7 is updated yearly to catch up with the syllabus of NCERT.

The RD Sharma solutions can be downloaded online from the Career360 website and it doesn't charge you a penny for getting the online PDFs from its website.

**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 the cost of this material?

This material is available free of cost on Career360's website.

2. Does this follow the CBSE syllabus?

Yes, this material follows the CBSE syllabus.

3. Are there any hidden charges?

No, the entire material is made available for students on career 360's website free of cost. There are no hidden charges.

4. Can I solve NCERT questions after preparing from this material?

Yes, as RD Sharma and NCERT books use the same concepts students can solve those questions after preparing from this material.

5. Does Career360 have solutions for other exercises?

Yes Career360 has solutions for other exercises on their website. Students can access those materials by searching the book name and exercise number.

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