The figure shows the part of a plane in the first octant. It meets the axes at $A(6, 0, 0)$, $B(0, 3, 0)$ and $C(0, 0, 2)$, with lengths in metres. What is the shortest distance from the origin to the plane?

Fig. 1: A three-dimensional picture with the x, y and z axes. A triangle with vertices A on the x-axis at 6, B on the y-axis at 3 and C on the z-axis at 2 is shaded orange. It is the part of a plane in the first octant. The origin O is marked, and a dashed red segment from O meets the plane at a right angle.