Find, in terms of a and b $\overrightarrow{\text{OF}}$.

Find $\overrightarrow{\text{AF}}$.

Find the length of the rope.

Find $\text{FÂO}$, the angle the rope makes with the platform.

Find the position vector $\overrightarrow{\text{OS}}$ of the ship at time $t$ hours.

Show that $\mu =\frac{1}{13}$, and find the value of $\lambda$.

Find an expression for $\overrightarrow{\text{OD}}$ in terms of a, b and $\mu$.

Find the value of $m$.

Consider a unit vector $\mathit{u}$, such that $\mathit{u}=p\mathit{i}-\frac{2}{3}\mathit{j}+\frac{1}{3}\mathit{k}$, where $p>0$.

Point $\text{C}$ is such that $\overrightarrow{\text{BC}}=9\mathit{u}$.

Find the coordinates of $\text{C}$.

Find an expression for $\overrightarrow{\text{OD}}$ in terms of a, b and $\lambda$;

Express $\overrightarrow{\text{AB}}$ in terms of $m$.

Find $\overrightarrow{\text{CA}}\times \overrightarrow{\text{CB}}$.

Find $\overrightarrow{\text{CB}}$.

Deduce an expression for $\overrightarrow{\text{CD}}$ in terms of a and b only.

Hence find the area of the triangle $\text{ABC}$.

Given that area $\mathrm{\Delta }\text{OAB}=k(\text{area }\mathrm{\Delta }\text{CAD})$, find the value of $k$.

Find, in terms of a and b $\overrightarrow{\text{AF}}$.

Find the value of $t$ when the ship will be closest to the lighthouse.

An alarm will sound if the ship travels within $20$ kilometres of the lighthouse.

State whether the alarm will sound. Give a reason for your answer.