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Consider the point \(A(1, 4, 5)\) and the plane \(\mathscr{P}\) with Cartesian equation:$$ 2x - y + 2z + 1 = 0 $$
Show that the point \(H(-1, 5, 3)\) is the orthogonal projection of \(A\) onto the plane \(\mathscr{P}\).
Determine the distance from point \(A\) to the plane \(\mathscr{P}\).
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