A plane is expressed parametrically by
\[\mathbf{v} = \begin{pmatrix} 2 + 3u - v \\ -1 + 2u + v \\ 4 - u + 2v \end{pmatrix}.\]
Find the equation of the plane in the form
\[Ax + By + Cz + D = 0,\]
where \(A,\) \(B,\) \(C,\) \(D\) are integers such that \(A > 0\) and \(\gcd(|A|,|B|,|C|,|D|) = 1.\) Let's think step by step and output the final answer within \boxed{}.
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