2. x,y,z co-ordinates, Pythagoras' theorem in three dimensions.
The third dimension is usually described in terms of a new letter: z.
The direction and orientation of the three dimensions varies in a similar way to the way the direction of y varies in two dimensions between high school graphs and digital screen co-ordinates, so always check which way is what.
3. R,G,B co-ordinates for colour, other colour spaces.
You can map any three variables into three dimensions to help you think about them spatially (i.e. in physical space).
An example of this is mixing together Red, Green and Blue (RGB) colours to make any other colour.
Digital colour mixing is additive while analogue paint mixing is subtractive.
How does projected light mix?
There are other ways of mixing variables to make colours - for example Hue, Saturation and Brightness (HSB).
I often use HSB in digital work to make it easy to blend between colours - much easier than RGB. You can visualise colour using a colour wheel or a colour solid. Complementary colours are on opposite sides of the colour wheel.
One way of storing three dimensional information is using point clouds.
The output of three dimensional scanners is often in point clouds - a grid of positions, each with a depth value - think of Pin Art toys from the 1980's.
Another way of storing three dimensional data is to use Voxels (from the initial letters of volume and element, with the insertion of -x- for ease of pronunciation).
Voxels can be a super efficient way of storing three dimension information - used for everything from MRI scanners to Minecraft.