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Problem 561

Minimize the distance from a point \(p \in R^{n}\) to the hyperplane \(<\mathrm{x}, \mathrm{a}>+\mathrm{b}=0\) where \(\mathrm{a} \in \mathrm{R}^{n}\) and \(\mathrm{b} \in \mathrm{R}\). (Assume \(\left.\mathrm{a} \neq 0 .\right)\)

Expert verified

The minimum distance \(D(p)\) between the point \(p\) and the hyperplane \( + b = 0\) is given by \(\frac{|

- b|}{|a|}\), and the point \(x_0\) on the hyperplane closest to the point \(p\) satisfies \(

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