
Boat Vectors
A ship currently at position a is sailing on a straight course with velocity u. Simultaneously a submarine at position b manoeuvres to intercept the ship. If the ship maintains its straight course at all times, show that the intercept course is orthogonal to the direction (a  b) and that in order to the ship the submarine must have minimum speed
$\displaystyle \frac{\textbf{u} \times (\textbf{a}  \textbf{b})}{\textbf{a}  \textbf{b}} $.
I'm not too worried about this as I have the answers right in front of me; however the bit I am having trouble with is this part:
$\displaystyle \textbf{d} = $ intercept course $\displaystyle = \textbf{x}_{A}(t)  \textbf{b} = (\textbf{a}  \textbf{b})  \frac{\textbf{a}\textbf{b}^2}{\textbf{u} \cdot (\textbf{a}  \textbf{b})}\textbf{u} = \frac{(\textbf{a}  \textbf{b}) \times (\textbf{u} \times (\textbf{a}  \textbf{b}))}{\textbf{a}\textbf{b}^2} $
I don't understand how $\displaystyle (\textbf{a}  \textbf{b})  \frac{\textbf{a}\textbf{b}^2}{\textbf{u} \cdot (\textbf{a}  \textbf{b})}\textbf{u} = \frac{(\textbf{a}  \textbf{b}) \times (\textbf{u} \times (\textbf{a}  \textbf{b}))}{\textbf{a}\textbf{b}^2} $ and any help would be appreciated.