deletions | additions       diff --git a/4-Dimensions.tex b/4-Dimensions.tex  index 7253827..689ceb4 100644  --- a/4-Dimensions.tex  +++ b/4-Dimensions.tex 
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t_2 & x_2 & y_2 & z_2 \\  t_3 & x_3 & y_3 & z_3 \\  \end{vmatrix}  =\textbf{i}\begin{vmatrix} =  \textbf{i}\begin{vmatrix}  x_1 & y_1 & z_1 \\  x_2 & y_2 & z_2 \\  x_3 & y_3 & z_3 \\  \end{vmatrix}  +... -  \textbf{j}\begin{vmatrix}  t_1 & y_1 & z_1 \\  t_2 & y_2 & z_2 \\  t_3 & y_3 & z_3 \\  \end{vmatrix}  +  \textbf{k}\begin{vmatrix}  t_1 & x_1 & z_1 \\  t_2 & x_2 & z_2 \\  t_3 & x_3 & z_3 \\  \end{vmatrix}  -  \textbf{l}\begin{vmatrix}  t_1 & x_1 & y_1 \\  t_2 & x_2 & y_2 \\  t_3 & x_3 & y_3 \\  \end{vmatrix}  \end{equation}  Therefore \begin{equation}