# Talk:Extra:Intersecting planes

## Rotate about

In general, rotation of a vector about an arbitrary unit-vector gives (1, 2):

In this particular case, we thus expect:

## Rotate about

In general, rotation of a vector about an arbitrary unit-vector gives (1, 2):

In this particular case, we thus expect:

## Generalized distance between two vectors

**Warning: Errors below** (this is just intermediate/working stuff)

Imagine reciprocal-space scattering that is a ring; more specifically a pseudo-toroid with Gaussian-like decay. The intensity overall is:

Where we use the subscript *r* to denote the reciprocal-space coordinate system, and . The plane of the detector (i.e. the Ewald plane) is denoted by *d*:

We set the symmetry axis in realspace (detector coordinate system) to be the -axis. The reciprocal-space is tilted by (about the -axis), before the 'powder' rotation about the -axis (where goes from to ). Consider an initial vector:

The 1st rotation (about -axis by ) involves:

Consider a 2nd rotation around the vector (normal to the detector plane) (**Warning: This is erroneous since the alpha rotation is just another phi rotation.**):

So the second rotation yields: