 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]

<div class="math-header">A Cross Product Formula</div>

\[\mathbf{V}_1 \times \mathbf{V}_2 =  \begin{vmatrix}
\mathbf{i} &amp; \mathbf{j} &amp; \mathbf{k} \\
\frac{\partial X}{\partial u} &amp;  \frac{\partial Y}{\partial u} &amp; 0 \\
\frac{\partial X}{\partial v} &amp;  \frac{\partial Y}{\partial v} &amp; 0
\end{vmatrix}  \]

<div class="math-header">The probability of getting \(k\) heads when flipping \(n\) coins is</div>

\[P(