Each problem of NCERT Solutions Class 11 Chapter 12 Introduction To Three Dimensional Geometry empowers the student to solve the problems in a dynamic way of consuming less time. The NCERT Solutions are written by the most experienced teachers making the clarification of every problem straightforward and reasonable. The students can refer to this pdf for the best exam preparation.
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NCERT Solutions for Class 11 Maths Chapter 12- Introduction to Three Dimensional Geometry
Given below are the topics of Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry
This section introduces the concept of coordinate axes, coordinate planes in real life, coordinates of the point concerning the three coordinate planes, basics of geometry in three dimensional space.
12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space
This section defines the rectangular coordinate system, naming of a coordinate plane and different notations in coordinate planes.
Rahul was riding his bicycle back home from a basketball game from a nearby stadium when he hit the divider to avoid a dog which had run onto the road. Unfortunately, his bicycle was stuck to the divider. When he couldn’t remove the bicycle by himself, he decided to take the help of his friend who stayed nearby. Rahul later looked at a topographical map and identified his friend’s house. He travelled 200 metres south and 550 metres west from where he left his bicycle. The map showed that he had also walked uphill from an altitude of 600 metres to an altitude of 650 metres above sea level. If we treat the location of Rahul’s bicycle as the origin of coordinates, what is the position vector of the Kapur farm?
12.3 Coordinates of a Point in Space
This section explains the coordinate system in space, coordinates [x, y and z] with few examples.
If a student is planning to place different pieces of furniture in a drawing-room, a two-dimensional grid representing the room can be drawn and an appropriate unit of measurement should be used. Let horizontal distance be x, and the vertical distance to x be y, and origin is the starting point. If the width of the room is 10 meters, any point in the room can be defined as (x,y,z).
12.4 Distance between Two Points
This section covers the distance between three points in a three-dimensional coordinate system using distance formula along with few solved problems.
If an object P is placed in the coordinate plane, the distance between the point P from the three axes [x,y and z] can be calculated using the distance formula.
12.5 Section Formula
This section talks about section formula for a three dimensional geometry and its different cases. A few examples are solved for better understanding.
Exercise 12.1 Solutions 4 Questions
Exercise 12.2 Solutions 5 Questions
Exercise 12.3 Solutions 5 Questions
Miscellaneous Exercise On Chapter 12 Solutions 6 Questions
A few points on Chapter 12 Introduction To Three Dimensional Geometry
- In three dimensional geometry, a cartesian coordinate system consists of three mutually perpendicular lines namely x, y and z-axes. They are measured in the same unit of length.
- The three planes XY-plane, YZ-plane and ZX-plane are determined by the pair of axes called the axes of the coordinate planes.
- The three coordinate planes divide the space into eight parts known as octants.
- The coordinates of a point P (x, y, z) in three dimensional geometry is written in the form of an ordered triplet. Here x, y and z are the distances from the YZ, ZX and XY-planes.
- (i) Any point on the x-axis is represented as (x, 0, 0)
(ii) Any point on the y-axis is represented as (0, y, 0)
(iii) Any point on the z-axis is represented as (0, 0, z).
- The coordinates of the point R divide the line segment joining two points P (x1,y1,z1) and Q (x2,y2,z2) internally and externally in the ratio m:n.
The solutions provide alternative methods and explanations to solve problems which make the student feel confident while facing the exam. Also, solving many complicated problems enhances the mathematical ability of the students. The solutions cover all the necessary questions, which a student must and should have mastered to appear for the exam. The BYJU’S subject experts who have prepared these solutions have years of understanding about the question paper setting and types of questions can be seen in these solutions pdf as given above.