Two baseballs are thrown horizontally from the top of a tall tower. The baseballs are thrown simultaneously with velocities \(\vec{v}_{01}=(3,1,0) ~\text{m/s}\) and \(\vec{v}_{02}=(-4,2,0)~\text{m/s}\).
Find the distance in meters between the baseballs when their velocities become perpendicular. You may ignore the air's resistance and assume \( \vec{g}=(0,0,-9.8)~\text{m}/\text{s}^{2}\).

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