The exercises in this chapter are divided into three parts - exercise 11.1, exercise 11.2 and 11.3. There is also a miscellaneous exercise that consists of different types of questions that are important in this chapter.
The following offers a brief idea of the topics that are covered in each of these exercises –
Class 12 Maths Chapter 11 Exercise 11.1
Ex 11.1 Class 12 consists of 5 questions and intends to test student’s knowledge of the fundamental concepts of three-dimensional geometry.
To solve the problems covered in this exercise, students need to be familiar with concepts viz. –
The three coordinate axes.
Method of finding the direction of cosines.
Class 12 Maths Chapter 11 Exercise 11.2
Ex 11.2 comprises a total of 17 questions that require students to solve equations, find values and prove different types of problems.
Students need to cover these topics mentioned below in details to be able to solve the problems accurately –
Direction of cosines
Direction ratio of a given line
Direction cosines of a line passing through two given points
Vector and Cartesian equations
The method to find an angle between two lines
Equation of lines in space
Class 12 Maths Chapter 11 Exercise 11.3
This exercise comprises of 14 problems, which also require students to solve equations to find value and direction of different points and angles.
To answer this section of the exercise accurately, individuals should be thorough with these concepts of Class 12 Maths Chapter 11 -
The method of finding the angle between two planes.
Method of finding the distance between two lines.
Method of finding the distance between skew lines.
Method of finding the distance between parallel lines.
Method of calculating the distance between a plane and a line.
Coplanarity of any two lines.
The angle between a line and a plane.
Equations of a plane and its interception.
Equations of a given line that passes through two particular points.
Equations of lines passing through a particular point and a parallel to any given vector.
NCERT Class 12 Maths Chapter 11 - Miscellaneous Exercise
This section comprises of 23 questions in total. Students need to be thorough with the concepts of three-dimensional geometry chapters to solve the problems effectively.
With regular practice, students will be able to tackle challenging problems easily and would be able to solve them in no time.
In case you require some help solving the problems more effectively or want to learn short-cut techniques, you can refer to our solutions for a better understanding.
By practicing our NCERT Solutions for Class 12 Maths Chapter 11 miscellaneous exercise frequently, students would be able to develop a better approach for solving equations efficiently and more accurately. This practice will come in handy for students while revising for their upcoming board examination in 2019-2020.
Similarly, by learning how to approach important questions better, students will able to able to score high in the subject.
Download our Three Dimensional Geometry Class 12 NCERT Solutions to kick-start your board exam preparation instantly!
Three Dimensional Geometry Class 12 - In Brief
The said chapter refreshes the basic concepts of vectors introduces students to newer concepts of three-dimensional geometry. Students will also learn about the different ways of finding the direction of cosines and ratios and will also be introduced to the Cartesian and vector equation of a line.
By understanding the concepts discussed in this chapter, students will not only be able to perform better in their upcoming examination but will also benefit in their higher studies.
Download a free PDF version of 3D Geometry Class 12 NCERT Solutions from our learning portal and enhance your understanding of the chapter in detail.
At Vedantu, we aim to make learning fun and easy by extending compact study solutions formulated by our experienced faculty. Students can access PDF free downloads of CBSE NCERT books and chapter-wise solutions as per the latest syllabus of all subjects online.
Our interactive learning portal is easy to use and fun to navigate. Students can access our compact chapter-wise solutions like Three Dimensional Geometry Class 12 NCERT Solutions PDF download on any device without going through any hassles.
At Vedantu, we extend well-crafted study materials for all standards that are updated as per the syllabus. Also, study materials like CBSE NCERT books, NCERT syllabus, and subject-wise solutions are designed in makes learning more convenient and productive.
Widen your scope of knowledge by joining our user-friendly and interactive learning portal and gain a better understanding of different subjects and their concepts all in one place.
Download Vedantu App today and venture into a world of real knowledge!
Share your contact information
Vedantu academic counsellor will be calling you shortly for your Online Counselling session.