deletions | additions       diff --git a/Sketchy Generation.tex b/Sketchy Generation.tex  index 5b4de48..9865b81 100644  --- a/Sketchy Generation.tex  +++ b/Sketchy Generation.tex 
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\begin{bmatrix} z_1y_2-y_1z_2 \\ x_1z_2-z_1x_2 \\ y_1x_2-x_1y_2 \end{bmatrix}  =-\textbf{r}_1 \times \textbf{r}_2  \end{equation}  \section{Cross Products}  We have the usual formula for a cross product \begin{equation}  \textbf{a} \times \textbf{b} = \epsilon_{ijk}a_ib_j\hat{\textbf{e}}_k  \end{equation}  with $e$ as the unit vectors. However from our determinant representations we could try writing \begin{equation}  \begin{vmatrix}  \textbf{i} & \textbf{j} & \textbf{k} \\  a_1 & a_2 & a_3 \\  b_1 & b_2 & b_3   \end{vmatrix}  =  \begin{vmatrix}  \textbf{i} & \textbf{j} & \textbf{k} \\  \textbf{i} & \textbf{j} & \textbf{k} \\  \textbf{i} & \textbf{j} & \textbf{k}   \end{vmatrix}  _{ijk}  a_ib_k\hat{\textbf{e}}_k  \end{equation}