Vector formula practice

Now I am sure that the multiplexing of all the things I study are starting to create random expression problems when I document. "practice and practive", I wonder if that v was for vector? The mind is a chaos approximation engine.

Wikipedia has a very good reference to using equations in HTML and La^Tex.

\overbrace{Vector\ properties}^{La^Tex\  reference} \ \ \ \begin{cases}
Scalar \  |\stackrel{\rightarrow}{A}| \\
Vector \stackrel{\rightarrow}{A} \\
dir(\stackrel{\rightarrow}{A}) = direction \\
det(\stackrel{\rightarrow}{A},\stackrel{\rightarrow}{B}) \\
\begin{bmatrix}a_1,a_2 \\ b_1,b_2\end{bmatrix} \\
det=(a_1\times b_2)-(a_2\times b_1) \\
det= \\
\hat A \times \hat B = \hat C \\
vec\  \vec A \\
dot\ is\  \dot{x} \\
Double dot\ is \  \ddot{A} \\
bar\ is\  \bar B \\
b\times h \times cos(\theta) \\
(\vec A \cdot \hat B)
\end{cases}

The goal is to have the documentation, that is in the program, display the description of a specific code sequence with the proper mathematical language. These things can be very complex and it is not just Nuclear physics or Astronomy that makes this difficult to use. OpenGL and AI for a game that is real time over a UDP connection can involve mathematics, methods, and concepts that are more complex than the most sophisticated equations of a neutron star collapse. Just incorporating light and its refraction, reflection and interference can branch to infinity very quickly.

I hope to have 'espeak' integrated well enough to allow the merging of a phoneme based language into the videos, so that in addition to speaking in the native language of the program user, it puts that audio in the video recording in a language specified with a speaker designation from a set of phoneme objects which is derived from Fourier analysis and recomposition.