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The dot product of the ellipsoid

The dot product is defined as

δi = $\displaystyle \widehat{{XH}}$⋅$\displaystyle \widehat{{\mathfrak{D}_i}}$, (15.170)

where i is one of {x, y, z}, $\widehat{{XH}}$ is a unit vector parallel to the XH bond vector, and $\widehat{{\mathfrak{D}_i}}$ is one of the unit vectors defining the diffusion frame. The three diffusion frame unit vectors can be expressed using the Euler angles α, β, and γ as

\begin{subequations}\begin{align} \widehat{\mathfrak{D}_x} &= \begin{pmatrix} -\... ...beta \sin \gamma \\ \cos \beta \\ \end{pmatrix}. \end{align}\end{subequations}


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