NCERT Solutions for Complex Numbers and Quadratic Equations Exercise 5.3 Class 11 Maths

September 13, 202239 Insightful Publications

**NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry: **NCERT Solutions are important for students. With the help of these solutions, they will learn about the representation of points and different three-dimensional figures. They will also learn about the salient features of three-dimensional shapes and their characteristics in detail. These NCERT Class 11 Maths Solutions by Embibe are based on the latest syllabus by CBSE.

Embibe provides NCERT Solutions for this chapter for free to students. These NCERT Solutions help students learn the correct method to solve exam questions. Apart from these solutions, Embibe also offers 200+ practice questions from this chapter covering 16 concepts. These practice questions are helpful as they increase students’ knowledge. Therefore, students must go through them to ace exams.

Students can clear their doubts by referring to NCERT Solutions for Class 11 Maths. Also, these Class 11 Maths Chapter 12 Solutions cover all the important topics from Three Dimensional Geometry. The important topics from Chapter 12 will teach students the fundamentals of geometry in three dimensions. Students must be familiar with coordinate geometry to understand the concepts of these topics.

The important topics include calculating the distance between two points, section formula, and many more. NCERT 11th Maths Chapter 12 Solutions comprise 14 questions. Talented subject matter experts at Embibe design these solutions to help students score better marks. Further, Embibe offers NCERT Exemplars and books for free. Students can also access free 3D videos at Embibe’s Learning Platform to understand concepts in-depth. These study materials are very helpful during exam preparation.

Now, let us look at the important topics from this chapter:

Sr. No. | Topic Name |
---|---|

12.1 | Introduction |

12.2 | Co-Ordinate Axes and Co-ordinate Planes in Three Dimensional Space |

12.3 | Coordinate of a Point in Space |

12.4 | Distance Between Two Points |

12.5 | Section Formula |

Some of the important points to remember from this chapter are as follows:

- Distance between two points A( x
_{1 }, y_{1 }, z_{1}) and B( x_{2 }, y_{2 }, z_{2}): √[(x_{2}– x_{1 })^{2}+ (y_{2}– y_{1})^{2}+ (z_{2}– z_{1})^{2}] - Coordinates of mid-point of given line segment that joins the two points A( x
_{1 }, y_{1 }, z_{1}) and B( x_{2 }, y_{2 }, z_{2}) are [ (x_{1}+ x_{2})/2, (y_{1}+ y_{2}/2) , (z_{1}+ z_{2}/2) ] - The coordinates of centroid of triangle and their vertices are (x
_{1 }, y_{1 }, z_{1}) , (x_{2 }, y_{2 }, z_{2}) and (x_{3}, y_{3}, z_{ 3}) are [ (x_{1}+ x_{2}+ x_{3})/3, (y_{1}+ y_{2}+ y_{3}/3) , (z_{1}+ z_{2}+ z_{3}/3) ] - Midpoint of a Line Segment: [½ (x1 + x2), ½(y1 + y2), ½(z1 + z2)]
- Coordinates of Centroid of a Triangle: [⅓ (x1 + x2 + x3), ⅓ (y1 + y2 + y3), ⅓ (z1 + z2 + z3)]

NCERT Solutions for Class 11 Maths are listed below to help students with their exam preparations:

**1st Chapter: Sets****2nd Chapter: Relations and Functions****3rd Chapter: Trigonometric Functions****4th Chapter: Principle of Mathematical Induction****5th Chapter: Complex Numbers and Quadratic Equations****6th Chapter: Linear Inequalities****7th Chapter: Permutations and Combinations****8th Chapter: Binomial Theorem****9th Chapter: Sequences and Series****10th Chapter: Straight Lines****11th Chapter: Conic Sections****12th Chapter: Introduction to Three Dimensional Geometry****13th Chapter: Limits and Derivatives****14th Chapter: Mathematical Reasoning****15th Chapter: Statistics****16th Chapter: Probability**

**Ans: **Students learn about various topics such as representing a point in three-dimension, cube, cuboid, cone, volume and area of three-dimensional shapes, and much more.

**Ans: **Students can get NCERT Class 11 Maths Chapter 12 Solutions at Embibe for free.

**Ans: **There are four exercises in NCERT Class 11 Maths Chapter 12 Solutions.

**Ans: **Yes, Embibe provides mock tests for Class 11 Maths Chapter 12 for free.

**Ans: **There are 14 questions in NCERT Class 11 Maths Chapter 12 Solutions.