The Visual Representation of a Cartesian 3D Axis System

In summary, the conventional way to draw a Cartesian 3D-axis-system is to have the z-axis pointing up and the y-axis angled anti-clockwise from the x-axis, in order to align with the perspective of 2D graph paper and the cross-product operation. This is drawn from the viewpoint of someone in the positive x and z sectors and negative y sector. The reason for this placement is not specified.
  • #1
Valianth
1
0
How do you draw an Cartesian 3D-axis-system?
The Y-axis seems to have some perspective; what's the position of the observer?
What's the 'way' of placement, and why?

All 'links' are welcome.

Dank u.
 
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  • #2
Welcome to PF!

Hi Valianth! Welcome to PF! :smile:

The convention is that you draw the z-axis up, and the y-axis anti-clockwise from the x-axis … but at an angle, so that it "looks" 3D! :smile:

This is so that it agrees with the usual way of looking at 2D graph paper. And so that the cross-product (i x j = k) looks right!

And you draw it from the perspective of someone in the x and z positive and y negative sector. :smile:

… why were you asking?
 

FAQ: The Visual Representation of a Cartesian 3D Axis System

What are 3D Cartesian coördinates?

3D Cartesian coördinates, also known as rectangular coordinates, are a system of describing the position of a point in three-dimensional space using three numbers representing the distances from three perpendicular axes.

How are 3D Cartesian coördinates different from 2D Cartesian coördinates?

3D Cartesian coördinates include a third axis, typically represented by the letter "z", in addition to the x and y axes used in 2D Cartesian coördinates. This allows for the representation of points in three-dimensional space, rather than just on a flat plane.

What are the three axes used in 3D Cartesian coördinates?

The three axes used in 3D Cartesian coördinates are the x-axis, y-axis, and z-axis. These axes are perpendicular to each other, forming a right-handed coordinate system.

How are points represented in 3D Cartesian coördinates?

In 3D Cartesian coördinates, points are represented by an ordered triple (x, y, z), where x represents the distance along the x-axis, y represents the distance along the y-axis, and z represents the distance along the z-axis. This is also known as the (x, y, z) coordinate of the point.

What is the purpose of using 3D Cartesian coördinates?

3D Cartesian coördinates are commonly used in mathematics and science to describe the position of objects in three-dimensional space. This is useful in fields such as physics, engineering, and computer graphics, where understanding the spatial relationships between objects is important.

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