PythonPlot (2) ThreeOrthogonalVectors

# Python #Plot

All the python study code can be found in my own repository.

## Purpose

When we describe the angle of an vector in 3d space, we will use three vectors to describe them. When We have three orthogonal vectors, how can be describe them and show them via plot? This is the purpose of this note.

To plot three orthogonal vectors in a 3d space. We will use three parameters to describe them.

1. $\theta$: the polar angle, angle between the c axis and the z axis
2. $\phi$: the azimuthal angle
3. Ratio_xy : to rotate the other two orthogonal vectors

I will begin from the special c-axis and it can be described by the polar angle $\theta$ and the azimuthal angle $\phi$ . The two other vectors are in the plane orthogonal to c-axis they can rotate in the plane. We can describe them via a ratio $R_{xy}$. The three vectors can be expressed as

where the $\hat{}$ are used to express the normalized vectors. It’s easy to check that the three vectors defined above are orthogonal to each other.

Author: Knifelee