Two submarines S ₁ and S ₂ , are travelling through the ocean.

They both appeared on the radar screen of a tracking station at the same time. The distances are measured in hundreds of meters and the time, t, in seconds, is measured from the instant they were both observed on the radar screen of the tracking station.

S ₁ : r ₁ = (2t - 4) i + (t - 15) j + (t + 5) k

S ₂ : r ₂ = 10 i + (-2t + 6) j + (2t - 2) k

Suppose that S ₁ and S ₂ continue to travel according to the above vector equations.

(i) Show further that S ₁ and S ₂ , will eventually collide at some point P, and further determine the coordinates of P.

(ii) Calculate, to the nearest meter, the distance between S ₁ and S ₂ , when they first observed by the tracking station.