The dot product of the spheroid

The single dot product of the spheroid is defined as

δz = $\displaystyle \widehat{{XH}}$$\displaystyle \widehat{{\mathfrak{D}_{\scriptscriptstyle \parallel}}}$, (15.181)

where $ \widehat{{XH}}$ is a unit vector parallel to the XH vector. $ \widehat{{\mathfrak{D}_{\scriptscriptstyle \parallel}}}$ is a unit vector parallel to the unique axis of the diffusion tensor and can be expressed using the spherical angles where θ is the polar angle and φ is the azimuthal angle as

$\displaystyle \widehat{{\mathfrak{D}_{\scriptscriptstyle \parallel}}}$ = $\displaystyle \begin{pmatrix}\sin \theta \cos \phi \\  \sin \theta \sin \phi \\  \cos \theta \\  \end{pmatrix}$. (15.182)

The relax user manual (PDF), created 2016-10-28.