Study MaterialsNCERT Exemplar SolutionsClass 12MathsNCERT Exemplar Solutions for Class 12 Maths Chapter 11 – Three Dimensional Geometry

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

Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and preparing for exams like JEE.

    Fill Out the Form for Expert Academic Guidance!



    +91

    Verify OTP Code (required)


    I agree to the terms and conditions and privacy policy.

    The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.

    The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

    Do you need help with your Homework? Are you preparing for Exams? Study without Internet (Offline)
    ×

      Download PDF for Free.
      Study without Internet (Offline)



      +91



      Live ClassesBooksTest SeriesSelf Learning



      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.

      Class12_Maths_Chapter11(DE-27)

      The topics and subtopics covered in Chapter 11- Three Dimensional Geometry of NCERT Exemplar Solutions for Class 12 are as follows:

      11.1 Introduction

      11.2 Direction Cosines and Direction Ratios of a Line

      11.2.1 Relation between the direction cosines of a line

      11.2.2 Direction cosines of a line passing through two points

      11.3 Equation of a Line in Space

      11.3.1 Equation of a line through a given point and parallel to a given vector b.

      11.3.2 Equation of a line passing through two given points

      11.4 Angle between Two Lines

      11.5 Shortest Distance between Two Lines

      11.5.1 Distance between two skew lines

      11.5.2 Distance between parallel lines

      11.6 Plane

      11.6.1 Equation of a plane in normal form

      11.6.2 Equation of a plane perpendicular to a given vector, passing through a given point

      11.6.3 Equation of a plane passing through three non-collinear points

      11.6.4 Intercept form of the equation of a plane

      11.6.5 Plane passing through the intersection of two given planes

      11.7 Coplanarity of Two Lines

      11.8 Angle between Two Planes

      11.9 Distance of a Point from a Plane

      11.10 Angle between a Line and a Plane

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

      According to the new CBSE Syllabus 2021-22, the chapter Three Dimensional Geometry is part of the unit Vectors and Three–Dimensional Geometry in term II. It accounts for 14 of the total marks. This chapter includes three activities, as well as a random, practice to assist students to grasp the fundamentals of Three Dimensional Geometry. The following are some of the topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths:

      1. The cosines of the angles formed by a line with the positive directions of the coordinate axes are called the direction cosines of a line.
      2. If l, m, n are the direction cosines of a line, then l^2+m^2+n^2 = 1
      3. A line’s direction ratios are the numbers that are proportional to the line’s direction cosines.
      4. Skewed lines are lines that are neither parallel nor intersecting in space. They are positioned on distinct planes.
      5. Angle between skew lines is the angle formed by two intersecting lines drawn parallel to one other from any point (ideally through the origin).
      6. If l1 , m1, n1 and l2, m2, n2 are the direction cosines of two lines; and θ is the acute angle between the two lines; then cosθ = |l1l2 + m1m2 + n1n2|

      These are some of the topics covered in the three-dimensional geometry chapter. NCERT Exemplar Solutions can be used as a quick reference to help students understand complicated concepts. Refer to the NCERT Textbook and NCERT Exemplar Solutions of Class 12 Maths for further information on the chapter.

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

      Students who study Class 12 Three Dimensional Geometry utilizing the NCERT Exemplar Solutions will be able to comprehend the following:

      A line connecting two places has direction cosines and direction ratios. The shortest distance between two lines, coplanar and skew lines, and the Cartesian equation and vector equation of a line. A plane’s Cartesian and vector equations. The angle is formed by two lines, two planes, or a line and a plane. A point’s distance from a plane.

      Get the most Important Questions ofPhysics, Chemistry, Maths, and Biology

      FAQ

      What is three dimensional geometry in NCERT Exemplar Solutions for Class 12 Maths Chapter 11?

      It is an area of mathematics that deals with three-dimensional coordinate systems and the study of lines, points, and solid objects. It will teach students how to use the z-coordinate in conjunction with the x and y coordinates to identify the precise location of a point in three-dimensional coordinate planes.

      Is NCERT Exemplar Solutions for Class 12 Maths Chapter 11 the best study material for the students during revision?

      Yes, the NCERT Exemplar Solutions for Class 12 Maths Chapter 11 is the finest study material for students who want to easily revise complicated ideas. Each solution includes a reasonable explanation to assist pupils in learning. INFINITY LEARN's in-house team of professionals has framed the step-by-step answers to encourage students to think analytically. These solutions can also be compared to obtain an idea of what different options are available for solving textbook problems.

      Why Opt for Infinity Learn?

      In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.

      What are the important topics covered in Chapter 11 of NCERT Exemplar Solutions for Class 12 Maths

      The topics and subtopics covered in NCERT Exemplar Solutions for Class 12 Maths Chapter 11 are listed below: 11.1 Introduction 11.2 Direction Cosines and Direction Ratios of a Line 11.3 Equation of a Line in Space 11.4 Angle between Two Lines 11.5 Shortest Distance between Two Lines 11.6 Plane 11.7 Coplanarity of Two Lines 11.8 Angle between Two Planes 11.9 Distance of a Point from a Plane 11.10 Angle between a Line and a Plane.

      Infinity Learn App

      Now you can find answers to all your subject queries & prepare for your Exams on our Learning App – Infinity Learn.

      Chat on WhatsApp Call Infinity Learn