A tunnel is to be dug through a mountain in order to link two cities.

Digging at one end of the tunnel begins at the point with coordinates (-3,-3,9) and continues in the direction 2 i + 2 j - k .

The digging at the other end of the tunnel starts at the point with coordinates (-19,-7,-3) and continues in the direction 6 i + 3 j + 2 k .

Both sections are assumed to be straight lines.

The coordinates are measured relative to a fixed origin O, where one unit is 50 meters.

(i) Show that the two sections of the tunnel will eventually meet at a point P, and find the coordinates of this point.              

(ii) Find the total length of the tunnel.