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Revision Notes for Class 11 Mathematics Chapter 12 Introduction to Three Dimensional Geometry
Class 11 Mathematics students should refer to the following concepts and notes for Chapter 12 Introduction to Three Dimensional Geometry in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks
Chapter 12 Introduction to Three Dimensional Geometry Notes Class 11 Mathematics
Key Concepts
1. A point in space has three coordinates.
2. Three dimensional system is an extension of two dimensional system. Third axis z is added to XY plane. There are two possible orientations of x and y axis . These two orientations are known as left handed and right handed system.
Right handed system is used mostly.
3. In three dimension, the coordinate axes of a rectangular Cartesian coordinate system are three mutually perpendicular lines. The axes are called the x, y and z-axes.
4. The three planes determined by the pair of axes are the coordinate planes, called XY, YZ and ZX-planes
5. There are 3 coordinate planes namely XOY, YOZ and ZOX also calledthe XY-plane, YZ plane and the ZX plane respectively.
6. The three coordinate planes divide the whole space into 8 parts. Eachof these parts is called an ‘octant’. The octants are numbered as
7. To each point in space, there corresponds an ordered triplet(x,y,z) of real numbers. There is a one to one correspondence between the points in space and ordered triplet (x,y,z) of real numbers.
9. To each point in space, there corresponds an ordered triplet(x,y,z) of real numbers. There is a one to one correspondence between the points in space and ordered triplet (x,y,z) of real numbers.
10.If P(x, y, z) is any point in space, then x, y and z are perpendiculardistances from YZ,ZX and XY planes.
11.The coordinates of the origin O are (0,0, 0).
12.The coordinates of any point on the x –axis are of the type (x,0,0).
The coordinates of any point on the y –axis are of the type (0,y,0).
The coordinates of any point on the z –axis are of the type (0,0,z)
13. The x coordinate of the point in the YZ plane must be zero.
A point in the XY plane will have its z coordinate zero
A point in the XZ plane will have its y coordinate zero.
14. Three points are said to be collinear if the sum of distances between any two pairs of the points is equal to the distance between the third pair of points. Distance formula can be used to prove collinearity.
15. If we were dealing in one dimension then x=a is a single point and if it is two dimensions then it will be a straight line and in 3 D it’s a plane || to YZ plane and passing through point a.
16. The distance of any point from the XY plane = | z coordinate | and similarly for the other 2 planes.
17.A line segment is trisected means it is divided into 3 equal parts by 2 points R and S. This is equivalent to saying that either R or S divides the line segment in the ratio 2:1 or 1:2.
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CBSE Class 11 Mathematics Chapter 12 Introduction to Three Dimensional Geometry Notes
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Notes for Mathematics CBSE Class 11 Chapter 12 Introduction to Three Dimensional Geometry
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Chapter 12 Introduction to Three Dimensional Geometry Notes for Mathematics CBSE Class 11
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Chapter 12 Introduction to Three Dimensional Geometry CBSE Class 11 Mathematics Notes
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Notes for CBSE Mathematics Class 11 Chapter 12 Introduction to Three Dimensional Geometry
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