X Line in a 3D Graph

Date: 03/10/2001 at 16:22:38
From: jane pfaender
Subject: x, y, z coordinates

Is the x line on a graph, as drawn on a page, vertical or horizontal?

Thank you.

Date: 03/10/2001 at 18:09:03
From: Doctor Achilles
Subject: Re: x, y, z coordinates

Hi Jane,

Thanks for writing to Dr. Math.

There are two conventional ways to draw a 3D graph on paper.

Your first choice is this:

                    +y
                     |
                     |
                     |
                     |
                     |
                     |
  (-x)---------------|----------------+x
                     |
                     |
                     |
                     |
                     |
                     |
                    -y

Where +y is the positive direction and -y is the negative direction 
for y.

In this graph, z would be positive coming out of the page at you and 
negative going into the page. This is often drawn like this:

                    +y     -z
                     |     /
                     |    /
                     |   / 
                     |  /
                     | /
                     |/
  (-x)---------------|----------------+x
                    /|
                   / |
                  /  |
                 /   |
                /    |
               /     |
              +z    -y

Here the +z is understood to be coming out of the page and the -z is 
understood to be going in.

Your second choice is this:

                    +z     +y
                     |     /
                     |    /
                     |   / 
                     |  /
                     | /
                     |/
  (-x)---------------|----------------+x
                    /|
                   / |
                  /  |
                 /   |
                /    |
               /     |
              -y    -z

In this case, +x is to the right and +z is up.  -y is coming out of 
the page at you and +y is going into the page.

These are actually equivalent representations.

To see that they are, try doing this: hold up your right hand with 
your palm flat, your fingers extended, and your thumb pointing to the 
side. Point your thumb in the +x direction while pointing your fingers 
in the +y direction. Your palm will automatically be facing the +z 
direction in both systems. (Try it out for both systems.)

Notice that in both of these conventional representations, x is 
horizontal. But there are other equivalent representations that don't 
have x pointing horizontally. For example:

                    +x     -z
                     |     /
                     |    /
                     |   /
                     |  /
                     | /
                     |/
    +y---------------|----------------(-y)
                    /|
                   / |
                  /  |
                 /   |
                /    |
               /     |
              +z    -x

This is just another perspective on the same representation as the two 
conventional representations I showed you above. However, in the two 
conventional representations that I'm familiar with, x is always 
horizontal.

Hope this helps. If you have any other questions about this or any 
other math topics, please write back.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/