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RD Sharma Class 12 Solutions Chapter 29 - The Plane (Ex 29.9) Exercise 29.9

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Last updated date: 19th May 2024
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RD Sharma Class 12 Solutions Chapter 29 - The Plane (Ex 29.9) Exercise 29.9 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 29 - The Plane Exercise 29.9 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 29 - The Plane Ex 29.9 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.


RD Sharma Class 12 Solutions Chapter 29 is a bible for the students appearing for their Class 12 Maths exam. The solutions in this PDF are sorted in a student-friendly way. These solutions can aid the students in preparing for their maths exams. Experts who work with us have single-handedly made sure that students don’t find any issue while solving this exercise. The solutions are very well presented, in a step-by-step manner for better understanding. So, let’s move forward by understanding the basics of the chapter first.

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Competitive Exams after 12th Science

Topics covered under RD Sharma Class 12 Solutions Chapter 29 - The plane

What is a plane and how can it be determined in mathematical language?

A plane can be determined very easily, If any of the following is known,

  • The plane's normal and its distance from the origin are supplied, i.e., the plane's equation in normal form.

  • It is perpendicular to a specified direction and goes through a point.

  • It goes through three non-collinear sites that are specified.


Let’s now try to understand the equation of a plane in very simple language:

  •  The vector form of a plane equation in normal form is r. n^=d

  • Where r is the point's position vector on the specified plane, n is the normal unit vector from the origin to the plane, and d is the normal unit vector's length from the origin to the plane.

  •  lx+my+nz=d is the Cartesian form of the plane equation in normal form.

  • P(x,y,z) is any point on the provided plane, n is the normal unit vector from the origin to the plane, and l,m,n are the normal unit vector's direction cosines.

  • If the vector equation of the plane is r.(ai+bj+ck)=d, then the Cartesian equation of the plane is (ax+by+cz)=d. The direction ratios of the normal to the plane are a,b,c.


Equation of a plane passing through three collinear points

The vector form of the equation of the plane is:

 

Important: (r −a ).[(b −a)×(c−a)]=0 

 

Here a, b, c are the position vectors of the three non-collinear points on the plane, whereas, r  is the position vector of any point on the given plane.

FAQs on RD Sharma Class 12 Solutions Chapter 29 - The Plane (Ex 29.9) Exercise 29.9

1. What are the benefits for RD Sharma Class 12 Solutions Chapter 29 - The Plane?

There are several benefits to using RD Sharma Class 12 Solutions Chapter 12 - The plane:

  • A thorough understanding of the concepts included in the exercise

  • More practice of the questions based on the NCERT exercises

  • Several different types of questions to solve to be fully prepared for your Class 12 Math exam

  • Solutions are available just in case one finds himself/herself stuck in between a problem

  • A different yet simple way of solving problems

2. Where can I find other resources to understand more about Class 12 Chapter -29 - The Plane?

You can find other helpful resources to strengthen your preparation for your maths exam easily from https://www.vedantu.com/. These resources are available free of cost for all the students/parents/teachers and whoever else is willing to access them. The resources include detailed notes with examples and sample questions, RD Sharma solutions for each exercise and practise sheets to assess your preparation. These are all free of cost and all you need to do is sign-in on the website or the app and you can get started with your math exam preparation.

3. What is the use of studying Geometry in real life?

There are several uses of studying geometry in real life:

  • Art and mathematics are linked in a variety of ways. For example, the theory of perspective (a graphical representation of an image as seen by eyes on a flat surface) demonstrated that geometry involves more than only metric qualities of objects, and this perspective is the foundation of projective geometry.

  • Geometry is utilised in satellites in GPS systems to calculate the satellite's position and GPS location, which is determined by latitudes and longitudes.

4. Is RD Sharma Class 12 Solutions Chapter 29 - The Plane (Exercise 29.9) a difficult exercise?

No, exercise 29.9 is not a difficult exercise but a technical one. It requires a good amount of application skills. Geometry in general isn’t very difficult to comprehend. A few hours of practice every day, and you’re good to go. But if you still face issues in understanding the problems and solving them, then we suggest you refer to these notes https://www.vedantu.com/revision-notes/cbse-class-12-maths-notes-chapter-11-three-dimensional-geometry  curated by our professionals at Vedantu.

5. How can I score good marks in my Class 12 Maths exam?

You can score well in your Class 12 Maths exam by keeping in mind the following points:

  • Practice daily. No matter what, take out a few hours to practice maths daily, to brush up on your concepts

  • Solve previous years’ question papers. These papers help you figure out the pattern of the paper and help you evaluate your speed and revision time accordingly.

  • Make your notes so that you can refer to them briefly before taking the exam.

  • Do not panic as it can seem intimidating at first, but understanding the problems require peace of mind.