In the $xyz$-coordinate system, a massive particle is initially at rest on a plane whose equation is given below: $x + 2y + 3z = 0.$ The particle is launched with initial velocity $(v_x,v_y,v_z) = (-3,7,12)$. It travels under the influence of a gravitational acceleration of $(a_x,a_y,a_z) = (0,0,-10)$ until it intersects the plane once more.

When the particle intersects the plane for the second time, how far away is it from the launch point (to 3 decimal places)?

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