RS Aggarwal Class 12 Solutions Chapter-28 The Plane

Q: 4. What is the key difference between the vector and Cartesian equations of a plane, and which one is better for solving problems?

The vector form (e.g., r · n = d) is powerful for conceptual problems involving direction and geometric relationships. The Cartesian form (ax + by + cz = d) is generally more convenient for algebraic calculations, such as finding intercepts or the distance of a point with specific coordinates. The best method depends on the information given in the problem; if the question provides vectors, use the vector form, and if it provides coordinates, the Cartesian form is usually more direct.

Q: 5. Why is the normal vector so crucial when solving problems related to planes in 3D geometry?

The normal vector is crucial because it defines the unique orientation of a plane in three-dimensional space. A plane has infinitely many vectors lying on it, but only one direction perpendicular to it. This perpendicular direction, represented by the normal vector, is the key to solving almost all problems related to planes, such as finding the angle between two planes (by using their normals), calculating the distance of a point from a plane, and establishing conditions for parallelism and perpendicularity.

Class 12 RS Aggarwal Chapter-28 The Plane Solutions - Free PDF Download

The RS Aggarwal Solutions Class 12 The Plane for the chapter The Plane are provided to the students so that they can utilize it for their preparations for class 12 CBSE exams. All of these exercises mentioned in the chapter for Class 12 Maths have been solved by our experts and hence will prove to be very helpful when it comes to assisting the students in their exams. Students will easily be able to revise for their exams with the help of these solutions. That is probably one of the main reasons why the solutions provided by us at Vedantu are considered to be the most helpful to these students. You can definitely score some good marks in the board exams and also the entrance exams with these solutions.

Download RS Aggarwal Solutions Class 12 Chapter 28

The RS Aggarwal Solutions Class 12 Chapter 28 are meant to provide all the assistance that students might need in order to practice for their examinations. There are many different exercise questions in this particular chapter with the help of which students can get a proper introduction to planes and learn more about them without any hassle. Such exercises are going to help the students understand what they need to know about Equations of Planes and much more. The chapter also deals with other important things such as the Vector Form of a particular equation and also the properties which are exhibited by the Cartesian form of equation as well for the students to understand.

Their chapter consists of a total of many different exercise questions and the compilation makes the whole chapter which the students can practice properly to earn good marks. With practice and more effort, the students will be able to solve different challenging questions in the near future, no matter how difficult it is. By the thorough practice of this exercise and with the help of our solutions for the questions, the students can easily understand and grow their knowledge on the different topics which are related to the plane and know different methods and formulas as well. These solutions are provided in a PDF format and hence are very easy to download.

These exercises which are provided in the RS Aggarwal Class 12 Maths Chapter 28 solutions will be very helpful as certain references for the course in the textbook and hence the students can achieve some great marks with proper practice. Not to mention that these exercises might also help the students gain some knowledge on some other syllabus too. Learning more and more about the cross products of vectors and some other important topics will help students gain some knowledge on the topic and help them gain a deeper understanding of the chapter. We cannot stress enough the importance of the chapter and that is why these solutions are so important.

There are a total of 11 exercises present in the chapter and there are 181 questions in total. Some of these questions might be a bit simpler and some of these are pretty difficult as well. So, the students need to ensure that they have a deeper understanding of the chapter before they try and solve them. It is really important that the students get to practice more and more of these questions so that they can get accustomed to the challenging bits of the exercises. With more practice, students can definitely prepare well for their examination and hence be at the top of their class.

Get Class 12 Maths RS Aggarwal The Place Solution With Us

One of the best things about having the solutions of Class 12 Maths RS Aggarwal The Plane Solutions is that these solutions are written in a very simple manner and hence it is very simple to understand as well. Apart from that, the answers are detailed and hence will definitely be very easy to understand. All the solutions are pretty much compliant with the board of CBSE and so much more. Apart from that, we have also managed to make sure that the students get to clear all their doubts and that too at one particular place. Students can easily use our solutions as the reference for their future exams as these solutions are created to help students in the entrance exams. So, the efficiency of the students will definitely increase more and more with practice.

FAQs on RS Aggarwal Class 12 Solutions Chapter-28 The Plane

1. Where can I find reliable, step-by-step solutions for all exercises in RS Aggarwal Class 12 Maths Chapter 28, The Plane?

Vedantu provides comprehensive, exercise-wise solutions for RS Aggarwal Class 12 Maths Chapter 28, The Plane. These solutions are crafted by subject-matter experts to align with the 2025-26 CBSE syllabus, ensuring every step is clearly explained for correct problem-solving and easy understanding.

2. What are the main types of problems solved in RS Aggarwal Class 12 Chapter 28 on The Plane?

The solutions for Chapter 28 guide you through solving a range of problem types, including:

Finding the vector and Cartesian equations of a plane under various given conditions.
Calculating the angle between two planes using their normal vectors.
Determining the shortest distance of a point from a plane.
Finding the equation of a plane that passes through the intersection of two other planes.
Solving problems where a plane is parallel or perpendicular to a given line or another plane.

3. How do I solve for the equation of a plane that passes through three non-collinear points as per the RS Aggarwal method?

To find the equation of a plane passing through three non-collinear points A, B, and C with position vectors a, b, and c, you should follow these steps:
1. Determine two vectors that lie in the plane, for example, vector AB = (b - a) and vector AC = (c - a).
2. Calculate the normal vector (n) to the plane by computing the cross product of these two vectors: n = AB × AC.
3. The required equation of the plane is then given by the formula (r - a) · n = 0. This step-by-step method is clearly demonstrated in the solutions.

4. What is the key difference between the vector and Cartesian equations of a plane, and which one is better for solving problems?

The vector form (e.g., r · n = d) is powerful for conceptual problems involving direction and geometric relationships. The Cartesian form (ax + by + cz = d) is generally more convenient for algebraic calculations, such as finding intercepts or the distance of a point with specific coordinates. The best method depends on the information given in the problem; if the question provides vectors, use the vector form, and if it provides coordinates, the Cartesian form is usually more direct.

5. Why is the normal vector so crucial when solving problems related to planes in 3D geometry?

The normal vector is crucial because it defines the unique orientation of a plane in three-dimensional space. A plane has infinitely many vectors lying on it, but only one direction perpendicular to it. This perpendicular direction, represented by the normal vector, is the key to solving almost all problems related to planes, such as finding the angle between two planes (by using their normals), calculating the distance of a point from a plane, and establishing conditions for parallelism and perpendicularity.

6. How do the solutions explain the method for finding a plane that passes through the intersection of two other planes?

The solutions explain this using the 'family of planes' concept. If the equations of two intersecting planes are P₁ = 0 and P₂ = 0, then the equation of any plane passing through their line of intersection can be written as P₁ + λP₂ = 0, where λ is a constant. To find the exact equation, you use an additional condition given in the problem (like a point the plane passes through) to solve for the specific value of λ. This is a standard method in the RS Aggarwal textbook that simplifies the solving process.

7. What is a common mistake to avoid when calculating the shortest distance of a point from a plane?

A common mistake is incorrectly substituting the coordinates of the point into the plane's equation. The correct formula for the distance from a point (x₁, y₁, z₁) to the plane ax + by + cz + d = 0 is |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c²). Students often forget to take the absolute value of the numerator or miscalculate the magnitude of the normal vector in the denominator. The provided solutions carefully demonstrate each step to help avoid these errors.