Example of 3-D Coordinate System

Example: Graph x = 3 in R, R² and R³.  

Solution

In R we consist of a single coordinate system and thus x=3 is a point in a 1-D coordinate system.  In R² the equation x=3 tells us to graph all the points which are in the form (3, y).  This is a vertical line in a 2-D coordinate system. 

In R³ the equation X = 3 tells us to graph all the points which are in the form (3,y,z) .  If you go back and look at the coordinate plane points this is very identical to the coordinates for the yz-plane apart from this time we have x = 3 in place of x = 0.  So, in a 3-D coordinate system this is a plane which will be parallel to the yz-plane and pass via the x-axis at  x = 3

Here is the graph of x = 3 in R.

Here is the graph of  x =3 in R².

Finally, here is the graph of x =3 in R³.

Note: We have presented this graph in two diverse styles.  On the left we have got the traditional axis system and we're employed to seeing and on the right

We have put the graph in a box.  Both of the views can be suitable on occasion to help with perspective and so we'll frequently do this with 3D graphs and sketches.