Math — Vectors

\mathbf{a}\cdot\mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta

\mathbf{a}\times\mathbf{b} = |\mathbf{a}||\mathbf{b}|\sin\theta\,\hat{\mathbf{n}}

|\mathbf{a}| = \sqrt{a_x^2 + a_y^2 + a_z^2}

\hat{\mathbf{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}