# Right-handed coordinate systems

• ehrenfest
In summary, using right-handed coordinate systems is a convention that has practical implications in calculations and physical phenomena. It ensures consistency and avoids discrepancies in results. Choosing to use a left-handed coordinate system may lead to reversed signs and changes in the determinant operator and cross product. While some may view it as a mere labeling difference, it is a convention that holds significance in mathematics and physics.
ehrenfest

## Homework Statement

Everyone tells me that I should use right-handed coordinate systems. But no one tells me what happens if I don't. What is the danger of not using right-handed coordinate systems?

## The Attempt at a Solution

What do you mean? How exactly are you going to "use" left-handed coordinate systems?

It's a convention, nothing more. Your signs will be backwards in some calculations.

(The real reason has to do with the fact that the determinant operator is uniquely determined by a basis AND an orientation. If you choose a different orientation than everybody else, your determinant will be the negative of theirs. It's a convention, but it's a convention that really matters. I'm guessing that this doesn't mean anything to you, and you probably just want to label your axes differently when you're graphing stuff. If so, please disregard.)

cross product changes too (related to the change in determinant operator)
many things like electromagnetism etc... motivate the use of right hand system as just a convenient way to present certain physical phenomena. But at the end of the day, it is just matter of convention. nothing else

## 1. What is a right-handed coordinate system?

A right-handed coordinate system is a three-dimensional coordinate system where the axes are perpendicular to each other and follow the right-hand rule. This means that the x-axis points to the right, the y-axis points up, and the z-axis points towards the viewer.

## 2. How is a right-handed coordinate system different from a left-handed coordinate system?

A right-handed coordinate system follows the right-hand rule, while a left-handed coordinate system follows the left-hand rule. This means that the axes in a left-handed coordinate system are oriented in the opposite direction compared to a right-handed coordinate system.

## 3. What is the purpose of using a right-handed coordinate system?

A right-handed coordinate system is commonly used in mathematics, physics, and computer graphics to represent three-dimensional space. It allows for consistent and intuitive calculations and visualizations.

## 4. How is a point represented in a right-handed coordinate system?

In a right-handed coordinate system, a point is represented by three coordinates (x, y, z) that correspond to its position on the x, y, and z axes, respectively. The origin (0, 0, 0) is the point where all three axes intersect.

## 5. Can a right-handed coordinate system be rotated?

Yes, a right-handed coordinate system can be rotated around any axis without changing its orientation. This is known as a rigid transformation. However, the axes must maintain their original perpendicularity and orientation to remain a right-handed coordinate system.

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