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

The RD Sharma solutions are the all in one problem solver for all the CBSE students who are preparing to appear for the board exams. The Class 12 RD Sharma chapter 28 exercise 28.9 solution is advised to go through while practicing the chapter ‘The Plane.’ It helps you to get a brief understanding of the concept while providing excellent examples that help you to understand better. The RD Sharma class 12th exercise 28.9 is the most recommended book by teachers for the students of CBSE as it matches the level of NCERT.

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The Plane Exercise 28.9 Question 1

Answer :Hint :

Given : Point from the plane vector

Solution :

For the given plane

Vector,

Cartesian form is

We can write as,

The point given is

Which can be written as

We know that

So we get,

On further calculation

The Plane Exercise 28.9 Question 2

Answer : The given points are equidistant from the planeHint :

Given :

Two points and , plane

Solution :

Points given by the equation

Plane given by the equation

, where the normal is

We know, the distance of from the plane Is given by

Distance of from the plane

And,

Distance of from the plane

Units

The point are equidistant from the plane

The Plane Exercise 28.9 Question 3

Answer : The answer of the given question is 3 unitsHint :

Given :

Point

Plane

Solution :

We know, the distance of point from the plane

Is given by

Putting the necessary values

Distance of the plane from

Hence the distance of the plane from the plane is 3 units

The Plane Exercise 28.9 Question 4

Answer : The answer of the given question isHint :

Given : Plane: , which are at a distance of 2 units from the point

Solution :

The planes are parallel to they must be of the form

We know, the distance of point from the plane given by

According to the question, the distance of the plane from is 2 units

Hence the required planes are

The Plane Exercise 28.9 Question 5

Answer: The answer of the given question is that the points are equidistant from the planeHint :

Given :

Points

Plane

Solution :

We know that, the distance of points from the plane Is given by

Distance of from the plane

Distance of from the plane

The points are equidistant from the plane

The Plane Exercise 28.9 Question 6

Answer : The answer of the given question areHint :

Given :

Solution :

Since the planes are parallel to they must be of the form

We know, the distance of point from the plane is given by

According to the question, the distance of the plane from is 1 Unit

The required planes are

The Plane Exercise 28.9 Question 7

Answer : The answer of the given question is 5 UnitHint :

Given :

Points :

Plane :

Solution :

We know, the distance of point from the plane

Is given by

Putting the values

The distance of the point from the xy-plane is 5 unit

The Plane Exercise 28.9 Question 8

Answer : The answer of the given question is unitHint :

Given :

Points :

Plane : , which in Cartesian form

Solution :

and point

We know the distance of point from the plane

Is given by

Putting the values

The distance of the point from the plane,

The Plane Exercise 28.9 Question 9

Answer : The answer of the given question isHint :

Given : Points:

Solution :

The distance of the point from the origin

We know, distance of from the origin is

Putting values of

Required distance

Distance of the point from plane

We know, the distance of point from the plane

Is given by

Putting necessary values,

According to the question

[ Because distance cannot be negative]

The Plane Exercise 28.9 Question 10

Answer : The answer of the given question isHint :

Solution : Let be a point which is equidistant from the given plane. Then,

Therefore this is the required equation.

The Plane Exercise 28.9 Question 11

Answer : The answer of the given question is UnitsHint :

Given :

3 Point and the plane determine by the point

Solution :

The equation of the plane passing through is given by the following equation

According to questions

Putting these values

Distance of from

We know, the distance of point from the plane

Is given by

Units

The Plane Exercise 28.9 Question 12

Answer : The answer of the given question is unitsHint :

Given : Plane makes intercept -6,3,4 respectively on the coordinate axes

Solution :

The equation of the plane which makes intercept a, b and c with the x, y and z axes respectively is

Putting the values of a, b and c

Require equation of the plane

We know, the distance of the point from the plane

Is given by

Distance from the origin i.e.

Required distance

The length of the perpendicular from the origin on the plane

The Plane Exercise 28.9 Question 13

Answer :Hint :

Given :

Solution : Let us consider the equation of plane passing through the point be

(1)

The direction ratios of the normal to the plane are a, b and c

The equation of the plane are

Since the plane passing through the point is perpendicular the given plane

Therefore,

Now, eliminating a, b and c from (1), (2) and (3)

We get

Now using distance formula

The distance of the point from the plane is

The RD Sharma class 12th exercise 28.9 covers the chapter 'The Plane.' There are about 19 questions in this exercise that are extremely basic and simple and covers all the essential concepts that are mentioned below-

Intercept form of the equation

Distance of the point from the plane

Equation of plane passing through points

Points are equidistant from the plane

Equation of plane passing through three points

Listed below are a few reasons that gives a brief idea about why the RD Sharma class 12 solution of The plane exercise 28.9 is the best solution for mathematics:-

The RD Sharma class 12th exercise 28.9 is available online on the Career360 website for download, thus you don't have to visit any stores to buy the solution.

You just need to have a good internet connection and a digital device to download the RD Sharma class 12 solution chapter 28 exercise 28.9 which is available free of cost on the Career360 website.

The experts of mathematics prepare the questions of the RD Sharma class 12 chapter 28 exercise 28.9 which makes the questions trustworthy and helpful tips can also be referred in the book for an alternate way to solve the questions easily.

It has been found that most of the questions that are asked in the 12th board exams are similar to the ones that are provided in the RD Sharma solution, therefore having a thorough practice of the solution can help you score high in the exams.

The exercises given in the RD Sharma class 12th exercise 28.9 are divided into two levels so that the students can distinguish easily between the low level and high level questions and practice accordingly.

The RD Sharma solutions are the best study material for any students who have the ambition to score high marks in the board exams and therefore teachers of all the CBSE schools recommend making use of this solution to practice rigorously.

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1. Who can use this material?

CBSE students who want to gain in depth knowledge on the subject can use this material.

2. How can I use this material?

RD Sharma class 12 chapter 28 material can act as a guide for students for their preparation. This will help them save time and study efficiently for their exams.

3. Can I refer to this material for my homework?

RD Sharma class 12 chapter 28 material is comprehensive and contains step-by-step solutions. This can help students better understand the concepts and finish their homework easily.

4. Is this material updated to the latest version?

Yes, RD Sharma class 12 chapter 28 material is updated to the latest version and is available for free on Career360’s website.

5. From where can I access this material?

Career360 provides RD Sharma class 12 chapter 28 material for free on their website. Students can use it through any device with an internet connection.

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