Mathematics Lab Activity-19 Class XI

Mathematics Laboratory Activities on Three Dimensional Geometry for class XI students Non-Medical. These activities are according to the CBSE syllabus

Chapter - 11 

three dimensional geometry
Activity - 19

Objective

To explain the concept of octants by three mutually perpendicular planes in space.

Material Required

A piece of plywood, colored papers, scissors, wooden board, saw, wires, rulers, cutters, thin sheet of wood etc.

Theory

Three mutually perpendicular planes divide the space into eight parts known as octants.

Procedure

1. Cut out three squares sheets, each of size 30cm x 30cm from a piece of cardboard.

2. Paste chart paper of different colored on both sides of the sheets as shown in the figure 19.1, 19.2, 19.3

Figure 19.1

It Shows XY-Plane

Figure 19.2

It Shows YZ-Plane

Figure 19.3

It Shows XZ-Plane

3. Fix two sheets in such a way that they intersect orthogonally in the middle of each other.

4. Cut the third sheet into two equal rectangles.

5. Insert one rectangle from one side in the middle cutting the two orthogonally, and the other rectangle from the other side as shown in figure. 19.4

Figure 19.4

6. The space is divided into eight parts by these three sheets. Each part is called an octant.

7. Fix the model on a wooden board.

8. In one of the octant, fix rulers to represent the x- axis, y-axis, and z- axis.

9. Extend each of the axis piercing to the other side to represent XX’, YY’ and ZZ’.

10. Mark the point of intersection of XX’, YY’, and ZZ’ as the origin O.

11. Fix a rod perpendicular to the x y - plane at point P(x, y) and parallel to the z-axis

Figure 19.5

12. Fix a wire joining the origin to the upper tip P (a, b, c) of this perpendicular rod.

13. The distance of the point P on xy- plane with coordinates (a, b) from the origin =   

14. The distance of point P with coordinates P (a, b, c) in the space from the origin

=  

Observations

1. The three planes are intersecting at right angles at a point and they divide the space into eight parts. Each part is known as octant.

2. Distance of point (5, 4) on the xy plane from the origin is

3. Distance of point (3, 2, 1) from the origin is  

4. If we fix a wire perpendicular to any of the planes, the it will represent normal to that plane.

5. If two normals are drawn to any two of the planes, then these normals are perpendicular to each other.

Result

Three mutually perpendicular planes divide the space into eight parts known as octants. 

Applications

1. The model can be used to visualize the position and coordinates of a point in a space.

2. It can be used to explain the distance of the origin from a point in the plane or in the space.

3. It can also be used to explain the concept of a normal to a plane.

VIVA – VOICE

Q. 1. What are coordinate planes?

Ans. In three dimensional geometry, three planes determined by any of the pair of axes are called co-ordinate planes.

Q.2. What are octants?

Ans. Three co-ordinate planes divide the space into eight parts known as octants.

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