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Consider the point \(A(1, 2, 3)\) and the plane \(\mathscr{P}\) with the Cartesian equation:$$ 2x - 3y + 4z - 5 = 0 $$Let \(H\) be the orthogonal projection of point \(A\) onto the plane \(\mathscr{P}\).
Determine a parametric representation of the line \((AH)\).
Hence, determine the coordinates of the point \(H\).
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