3D Coordinates

INTRODUCTION

Hope you have enjoyed the tutorial on 2D Coordinates
In this tutorial, the concept of 3D coordinates is explained.

when we talk about 2D objects like a board or a wall, we use 2 dimensions.
For example, we say that a board is 10 feet wide and 2 feet high.

But, when we talk about 3D objects like a swimming_pool or a box, we will use 3 dimensions.
For example, we say that a swimming_pool is 5 feet deep, 10 feet wide and 20 feet long.
Apart from the x and y dimensions, a 3D point will also have one more dimension... Z.

In the following flash control, these 3 dimensions are visualized.
You can notice that the 3 sliders have 3 different colors.
If you move the red slider, the RED PLANE will move along the X-axis.
If you move the green slider, the GREEN LINE will move on the red plane, along the Y-axis.
If you move the blue slider, the BLUE POINT will move on the green line, along the Z-axis.

Feel free to drag the 3 sliders and see how the diagram gets modified accordingly.

NOTATION:
In 2D, we denote a point with 2 values (x, y)
In 3D, we denote a point with 3 values (x, y, z)

In the above diagram,
The 3D point (1, 0, 0) is denoted by v100.
The 3D point (0, 1, 0) is denoted by v010.
The 3D point (0, 0, 1) is denoted by v001.
Please note that the notation followed in such a way that, the 3D point (x, y, z) is denoted by vxyz.

QUESTIONS:

What is the 3D point represented by v110 ?
What are the two end points of the GREEN LINE for the given slider positions of x = 25%, y = 50% and z = 75% ?
What are the 3D coordinates for the front top corner of the RED PLANE for the slider value x = 50% ?

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