RD Sharma Class 12 Chapter 29 Solutions (The Plane)
RD Sharma Class 12 Maths Solutions Chapter 29 ‘The Plane’ teaches you the basics to the most complex issues of the topic Plane in mathematics. In this chapter you’re going to learn the definition of the plane, equations of a plane passing through a given point, algorithms, proving coplanarity of four points, intercept form of a plane, vector equation of a plane passing through a given point and normal to a given vector, equation of a plane in normal form, cartesian form, vector equation of a plane passing through three given points, the angle between two planes and a lot more. This is an interesting chapter with 15 exercises and 148 questions.
We have prepared exercise-wise solutions for RD Sharma Class 12 Chapter 29 ‘The Plane’ that will help you in solving all the questions of the chapter. Our solutions will help you prepare for CBSE exams along with entrance tests such as BITSAT, JEE Main and NEET Solutions. There are many complex topics in this chapter such as the condition of coplanarity of two lines and equation of the plane containing them, an alternative method for the shortest distance between skew lines and image of a point in a plane. You can understand all these complex topics easily with the help of our RD Sharma solutions.
Some topics discussed in RD Sharma Class 12 Maths Solutions Chapter 29 – The Plane
Definition of the Plane
Consider a surface and two points on that surface. That surface will be a plane if the line segment joining those two points will lie completely on that surface containing the two points.
Equation of a plane in Normal Form
Theorem on Cartesian form
Let l, m, n be the direction cosines of a given plane’s normal. This plane is present at a distance p from the point of origin. This gives the equation of the given plane as
lx + my + nz = 0
The angle between two Planes
The angle between the normals of the two planes is called the angle between the two planes.
Equation of a Plane passing through the intersection of two planes
A straight line forms when two planes intersect. For example, xy-plane and xz-plane intersect and form the x-axis. The plane that has the intersection line of the given planes will be known as the plane that passes through the point where the two planes meet.
Discussion of Exercises in RD Sharma Class 12 Maths Solutions Chapter 29 – The Plane
- The first exercise 29.1 includes questions on finding the equation of a plane passing through three given points, and proving coplanarity of four given points.
- The second exercise 29.2 discusses questionnaires on the intercept form of a plane.
- The third exercise 29.3 includes questions on the vector equation of a plane passing through a given point and normal to a given vector.
- The fourth exercise 29.4 talks about the equation of a plane in normal form, vector form, cartesian form, etc.
- The fifth exercise 29.5 talks about the vector equation of a plane passing through three given points.
- The exercise 29.6 talks about the angle between the two planes, on finding a plane passing through a given point and perpendicular to two given planes, on finding a plane that passes through two points and that is perpendicular to a given plane.
- The exercise 29.7 discusses finding the equation of a plane that passes through a given point and is found parallel to two vectors or lines
- The exercise 29.8 asks questions based on the equation of a plane that passes through the intersection of two given planes.
- Exercise 29.9 discusses the concept of the distance of a point from a given plane.
- The exercise 29.10 talks about the distance between the two parallel planes.
- The exercise 29.11 discusses line and a plane.
- Exercise 29.12 discusses the intersection of a line and a plane.
- The exercise 29.13 talks about the condition for a line to lie in a given plane.
- The exercise 29.14 discusses questions on alternative methods for the shortest distance between the two skew lines.
- The exercise 29.15 talks about the image of a point in a line.
Benefits RD Sharma Class 12 Maths Solutions Chapter 29 – The Plane by Instasolv
RD Sharma Class 12 Maths Solutions for Chapter 29 ‘The Plane’ explain all the major concepts related to the chapter in detail. We understand time management can be a serious problem with class 12 students so we have made it easier for you to get all your doubts in one place. For any further doubts related to the chapter, seek help from our experts right now and find instant solutions.