NCERT Exemplar Class 12 Maths Solutions for Chapter 11 - Three Dimensional Geometry

NCERT Exemplar Class 12 Maths Chapter 11 Three Dimensional Geometry, are provided here for students to practice and prepare for the exam. While students have already studied vector algebra in the previous chapter, they will apply this concept to three-dimensional geometry to further make the study simple. In chapter 11, students will mainly learn about three-dimensional lines and planes, the angle between two lines and also find equations in vector forms. Some of the other specific topics include direction cosines and direction ratios, the equation of a plane, etc.

Class 12 Maths NCERT Exemplar Problems for 3D Geometry

Here are the important topics covered in chapter 11:

  • Introduction
  • Direction Cosines and Ratios of a Line
  • Relation between the direction cosines of a line
  • Direction cosines of a line passing through two points
  • Equation of a Line in Space
  • Equation of a line via a given point and parallel to a given vector
  • Equation of a line passing through two given points
  • Angle between Two Lines
  • Shortest Distance between Two Lines
  • Distance between two skew lines
  • Distance between parallel lines
  • Plane Equation of a plane in normal form
  • The equation of a plane perpendicular to a given vector and passing via a given point
  • Equation of a plane passing through three non-collinear points
  • Intercept form of the equation of a plane
  • Plane passing by the intersection of two given planes
  • Coplanarity of Two Lines
  • Angle between Two Planes
  • Distance of a Point from a Plane
  • Angle between a Line and a Plane

Since there are a lot of topics to cover in this chapter, students can freely download and use NCERT exemplar problems with solutions for class 12 maths chapter 11, given here. These solved questions will help students to understand the whole concepts introduced in the chapter. Student’s can also use these as a reference while solving different types of 3-D geometry problems.

Students are provided with NCERT solutions for class 12th Maths also along with notes, question papers and other learning materials, online for free, prepared by the experts as per CBSE syllabus(2018-2019). Also, students are suggested to solve previous year question papers and sample papers of 12th class Maths subject, to know the question pattern and marking scheme for chapter Three Dimensional Geometry.


Visit BYJU’S and get all the updated learning materials along with 12th standard NCERT exemplar solutions. Students are suggested to download BYJU’S- The Learning App and get a more efficient and personalized learning experience with the help of educational videos explaining the concepts of topics like Three Dimensional Geometry.

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