# Introduction To 3D Space

- Author:
- Ajay Kumar Otta

ONE DIMENSIONAL SPACE

TWO DIMENSIONAL SPACE

THREE DIMENSIONAL SPACE

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Consider an ant moving on a tight thread fixed end to end horizontally from a wall to another wall in a room. Its movement is restricted to the thread only. We say it has one degree of freedom. Let us put the ant on the floor of the room. It has more freedom now . It can move on the floor in two directions. Still its movement is restricted to the floor. We say it has two degrees of freedom. Imagine now we are playing with a toy drone. The remote is in our hand. We can make it take off . It has more freedom than our ant. The space in which it can fly is three dimensional. It can fly in three mutually independent directions.
We live in a world of three dimensions. Most objects around us have length, breadth and height . If we want to study their shapes then we have to begin somewhere. The applet below shows three planes. The red plane is the horizontal one and the other two are vertical . The point where all of them intersect is the point where we begin. We shall call it as the origin and denote it by the letter O. The red plane is a two dimensional plane. We can see two lines intersecting each other at right angle. These two are the usual x and y axes. The red line is the x-axis. The green line is the y-axis. The line starting from O and perpendicular to the x-y plane will be taken as the z-axis. It is the blue line. It happens to be the intersection of the two vertical planes.
Any point in this space can now be identified with three coordinates with respect to these three axes.

Rotate the planes below and see that that the whole space is divided into 8 distinct portions. These are called octants. The first octant has points all whose coordinates will be positive.

## 3DimensionalGeometry

## In the applet below to move the point A vertically click it once and drag it upwards or downwards.To move it horizontally click it again and then drag horizontally . Observe how the coordinates change. You can rotate the planes as well.

## The Coordinates and the Coordinate planes

Note that the point A is denoted by a triplet . The last one is the z- coordinate. If we drag the point A to lie on the red plane. Then its z coordinate will become 0. Next if it is above the red plane its z coordinate will be positive and if it is below it will be negative.

## Q.1

How should we refer the y-z plane?

## Q.2

How should we refer the z-x plane?

## Q.3

In what way you can describe all the upper four octants?

## Q.4

In what way you would express the lower four octants?

## Drag the point B (Red) along the x-axis and study the coordinates of the eight vertices of the cube .

## Q.5

Which of the points below lie on the x-axis?

## Q.6

Which of the points below lie on the y-axis?

## Q.7

Which point below lies on the z-axis?

## Q.8

Which point below lies on the x-y plane?

## Q.9

Which point below lies on the y-z plane?

## Q.10

Which point below lies on the z-x plane?