Paul's Online Notes
Home / Calculus III / 3-Dimensional Space / The 3-D Coordinate System
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

### Section 12.1 : The 3-D Coordinate System

5. List all of the coordinates systems ($$\mathbb{R}$$, $${\mathbb{R}^2}$$, $${\mathbb{R}^3}$$) that the following equation will have a graph in. Do not sketch the graph.

${x^3} + \sqrt {{y^2} + 1} - 6z = 2$ Show Solution

This equation has three variables and so it will have a graph in $${\mathbb{R}^3}$$.

On other hand because the equation has three variables in it there will be no graph in $${\mathbb{R}^2}$$(can have at most two variables) and it will not have a graph in $$\mathbb{R}$$ (can only have a single variable).