# NCERT Exemplar Class 11 Maths Chapter 12 Solutions: Introduction to Three Dimensional Geometry

NCERT Exemplar Solutions for Class 11 Maths Chapter 12 deals with the distance formula and section formula as its primary concept. Other main topics of the chapter include coordinate axis and coordinate planes, coordinate of a point in space, and the sign of coordinates of a point. This chapter of NCERT Exemplar Class 11 Maths is the base of three-dimensional geometry which you will study in the higher classes. So, it is important for you to clear your concepts well.

Chapter 12 – Introduction to Three Dimensional Geometry consist of 3 exercises with a total of 87 questions. The different types of questions available in the exercise include short answer type, long answer type, objective type questions, fill in the blanks, match the following, and state true or false. By practising these questions, you can score good marks in your CBSE exams.

NCERT Exemplar Class 11 Maths Solutions Chapter 12 – Introduction to Three Dimensional Geometry are prepared after huge research by highly experienced maths teachers at Instasolv. Referring to these solutions will enhance your basic concepts, which in turn, results in solving the questions without mistakes. So, in order to score good marks, you are suggested to follow these NCERT Exemplar Solutions now.

## Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 12 – Introduction to Three Dimensional Geometry

**Coordinate Axis**

In any three-dimensional figure, the coordinate axis of a rectangular Cartesian coordinate system is represented by three mutually perpendicular lines. These axes are termed as x-axis, y-axis, and z-axis.

**Planes**

The three planes that are determined by the pair of the axis are the coordinate planes, called XY, YZ, and ZX planes.

- xy-plane, z = 0
- yz-plane, x = 0
- zx-plane, y = 0

**Octants**

When any three coordinate planes divide the space into eight parts that are known as octants.

**Points represented in 3D**

The coordinate of a point A in three-dimensional geometry is always represented as (x, y, z). Here, x, y, and z are the distances from the YZ, ZX, and XY.

- Any point on XY plane is denoted as (x, y, 0)
- Any point on YZ plane is denoted as (0, y, z)
- Any point on ZX plane is denoted as (x, 0, z)

**Section Formula**

The coordinates of M which divided a line segment joining the points A (x1, y1, z1) and B (x_{2}, y_{2}, z_{2}).

Internally and externally in the ratio p : q respectively

Internally: A {(px_{2} + qx_{1} / p + q), (py_{2} + qy_{1} / p + q), (pz_{2} + qz_{1} / p + q)}

Externally: B {(px_{2} – qx_{1} / p – q), (py_{2} – qy_{1} / p – q), (pz_{2} – qz_{1} / p – q)}

**Centroid**

The coordinates of the centroid of the triangle whose vertices are (x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), and (x_{3}, y_{3}, z_{3}) is {(x_{1} + x_{2} + x_{3} / 3), (y_{1} + y_{2} + y_{3} / 3), (z_{1} + z_{2} + z_{3} / 3)}

### Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 12 – Introduction to Three Dimensional Geometry

Chapter 12 – Introduction to Three Dimensional Geometry has a total of 3 exercises with 87 questions. The detailed description of these exercises is provided below:

**Exercise 8.1 – Short Answer Type Questions**

Exercise 12.1 of Chapter 12 – Introduction to Three Dimensional Geometry consists of a total of 17 short answer type questions. These questions are based on the important topics including coordinate axis and coordinate planes, coordinate of a point in space, and sign of coordinates of a point.

**Exercise 8.2 – Long Answer Type Questions**

This exercise consists of a total of 4 questions based on the primary concept like distance formula and section formula. They are long answer type questions where you will find detailed solutions to the problems. Practising these questions will help you clear your concepts on the introduction to three-dimensional geometry.

**Exercise 8.3 – Objective Type Questions**

It is the last exercise of NCERT Exemplar Solutions Class 11 Chapter 12 and is considered a very important exercise from the entrance exam point of view. It contains a total of 29 questions including fill in the blanks, state true or false, or multiple-choice questions. Solving the questions of this exercise will help you understand how clear your concepts are.

Also, there are around 37 solved examples in the chapter that are explained well for your future reference.

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