How far was the buoy from the ship, and at what bearing, at the time the ship initially left point O?  Give the distance in kilometers, and give your answers correct to 1 decimal place.

Find the magnitude of ${F}_{2}$ and the angle it makes with the vector i.  Give your answers correct to 1 decimal place.

By setting up and solving suitable vector equations, prove that each of BE and CD divides the other in the ratio 1:2.

In triangle ABC, D is the midpoint of AB and E is the midpoint of AC.  BE and CD intersect at point F.

Given that  $\overset{\rightarrow}{AB}=2a$ and  $\overset{\rightarrow}{AC}=2b$, write the vectors $\overset{\rightarrow}{BC},\overset{\rightarrow}{BE}$and $\overset{\rightarrow}{CD}$ in terms of a and b.