The Three-Dimensional Point in Detail

Do You Know What Three-Dimension Is?

So, what the 3 stands for in three dimensions are the directions of the three vectors in the Cartesian system. They are in three different directions, provided all the vectors don’t lie in the same plane or commonly these three vectors are named as length, breadth and width.

Locate a point in 3d space

In a Cartesian system, a point in three-dimensional space is represented by three coordinates (x, y and z). Three coordinates, the x-coordinate, y-coordinate and z-coordinate axes, are mutually perpendicular to each other, as shown in the figure. All three axes coincide at a point marked as (0, 0, 0). This point is also called the origin of all the  

measurements are taken while plotting a point. The position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is the same distance as the distance of that point from the plane fixed on by the other two axes.

The coordinate planes are: The XY-plane, the set of all points whose x-coordinate is zero; the yz-plane, the set of all points whose x-coordinate is zero; and the xz-plane, the set of all

points whose y-coordinate is zero.

HOW TO PLOT A POINT IN 3D SPACE

Let’s take the example given in the above figure and mark point P.

Firstly, to make this easy, let’s plot a point, (x, y), on the two-dimensional coordinate plane:

• Locate x on the x-axis(P)
• From that point, moving parallel to the y-axis, move y units(P); that is (x, y)

Now, while considering the point in three dimensions. To plot the point (x, y, z) in three dimensions, we simply need to consider the z-axis and do the same. That is, to plot a point (x, y, z) in three dimensions, we follow these steps:

• Find x on the x-axis
• From that point x, moving parallel to the y-axis, move y units
• From that point, moving parallel to the z-axis, move z units; this is (x, y, z)

 For example, plot the point (1, 2, 3) in three dimensions:

• First, we locate 1 on the x-axis
• Next, we move 2 units parallel to the y-axis
• Lastly, we move 3 units parallel to the z-axis

This gives you the point (1, 2, 3). It is very simple!

3D SHAPES

In simple terms, we can say that a 3D shape or object is a solid or it is something that has all three aspects, i.e. length, breadth and width. Every object we come across in our daily life is in 3D configuration. For example, some shapes that we commonly see are spheres, cones, cubes, cuboids etc., like we consider the earth to be a 3D sphere.

A characteristic 3D shape has faces, edges and vertices.

TYPES OF 3D SHAPES

The 3D shapes include curved solids, and with straight sides solids, also called polyhedrons, they have further subdivisions like polytopes, showing a more complex nature in space.

CURVED SOLIDS 

These include;

Sphere: It is a round solid represented in space with all points equidistant from the centre.

                A sphere has 1 curved surface, 0 edges, 0 vertices.

Cone: A solid with a circular base and one vertex

            A cone has 2 faces (circular base and curved surface), 1 vertex, 1 edge.

Cylinder: It is a parallel circular solid with curved surfaces joining together.              

                    A Cylinder has 3 faces, 2 edges, 0 vertices.

POLYHEDRONS

These include;

Cube: It has 6 square faces, 8 vertices and 12 edges

Cuboid: It has 6 rectangular faces, 8 vertices and 12 edges

Conclusion

We can conclude by saying that the three-dimensional system is the most significant system as we are surrounded by it. The earth we live in is able to only perceive and see 3D and lower dimensions. This article has given a basic idea of how a 3D coordinate system works and other advanced coordinate systems. This simply means every point in space has its coordinates and dimension; each point has its unique position and properties. Euclidean geometry has advanced more and more in the coming days as we still need to study our vast universe. We also got an idea of how 3D shapes are formed, different types of 3D shapes and their properties.