# Right-handed coordinate system

• ehrenfest
In summary, a right-handed coordinate system is a mathematical concept used to describe the position and orientation of objects in three-dimensional space. It consists of three axes - X, Y, and Z - that intersect at a 90 degree angle and is commonly used in physics, engineering, and computer graphics. The main difference between a right-handed and left-handed coordinate system is the direction in which the axes are oriented. The right-hand rule is a convention used to determine the direction of the cross product between two vectors in a right-handed coordinate system. It is used in physics because it allows for consistent and accurate mathematical calculations. However, a right-handed coordinate system is not the only way to describe three-dimensional space, as there are also left-handed coordinate systems
ehrenfest

## Homework Statement

Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet.

Is this true:

A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat

?

## The Attempt at a Solution

Last edited:
ehrenfest said:
A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat

Yes.
In a left-handed system, $\hat{x} \times \hat{y}= - \hat{z}$

## What is a right-handed coordinate system?

A right-handed coordinate system is a mathematical concept used to describe the position and orientation of objects in three-dimensional space. It consists of three axes - X, Y, and Z - that intersect at a 90 degree angle, forming a three-dimensional grid. This system is commonly used in physics, engineering, and computer graphics.

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

The main difference between a right-handed and left-handed coordinate system is the direction in which the axes are oriented. In a right-handed system, the positive X-axis points to the right, the positive Y-axis points upwards, and the positive Z-axis points towards the viewer. In a left-handed system, the positive X-axis points to the left, the positive Y-axis points downwards, and the positive Z-axis points away from the viewer.

## What is the right-hand rule in a right-handed coordinate system?

The right-hand rule is a convention used to determine the direction of the cross product between two vectors in a right-handed coordinate system. It states that if you point your right thumb in the direction of the first vector and your index finger in the direction of the second vector, then your middle finger will point in the direction of the resulting cross product.

## Why is a right-handed coordinate system used in physics?

A right-handed coordinate system is used in physics because it is a standardized way to describe the position and orientation of objects in three-dimensional space. It allows for consistent and accurate mathematical calculations and is commonly used in physical laws and equations.

## Is a right-handed coordinate system the only way to describe three-dimensional space?

No, a right-handed coordinate system is not the only way to describe three-dimensional space. There are also left-handed coordinate systems, as well as other coordinate systems such as cylindrical and spherical coordinates. The choice of coordinate system depends on the specific application and the convenience of using a particular system.

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