Too many calculations?

Geometry Level pending

If from a point \(P (4,4)\) perpendiculars to the straight lines \( 3x + 4y +5 = 0 \) and \(y=mx+7\) meet at \(Q \) and \(R\) respectively and area of \( \triangle PQR \) is maximum. Then the value of \(3333m\) must be?

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