An algorithm has been trained with a number of data points $($x$\_\{$i$\},$ y$\_\{$i$\},$ z$\_\{$i$\})$ and classifies each into "Category A$"$ or "Category B$"$ depending on what side of the plane x $+2$y $+$ z $=3$ the data point is on$.$ For instance, the point A$\_\{1\}(-2\mathrm{.}3,4,3\mathrm{.}3)$ is in Category A $($left figure$),$ the point B$\_\{1\}(-6,9,2,1,4\mathrm{.}6)$ is in Category B $($right figure$).$ In machine learning, the plane is called the "decision boundary $"$