[填空题]
The displacement of a remote-controlled toy yacht is modelled f. tx3hu8ft zxqko4+v:a+1nhby the vector ,x17teljlch9v 1r/ krge( ny* equatioglr1 vn lt1h/,xe*jkcy7r(e9n
$\mathbf{r}=\left(\begin{array}{c}
-5 \\
12
\end{array}\right)+t\left(\begin{array}{c}
1.5 \\
-2
\end{array}\right),$
where t is the sail time, in seconds, $ t \geq 0$ , and distances are measured in metres.
Ali is standing on a boat dock at $\mathrm{O}(0,0)$ and controls the yacht.
1. Write down the position of the yacht at :
(1). t=0 ;(a,b) a= b=
(2) t=3 .(a,b) a= b=
2. Determine the speed the yacht is travelling. $ms^{-1}$
3. Determine :
(1) the distance between Ali and the yacht at t=0 ; m
(2) an expression for the distance between Ali and the yacht for t \geq 0 .
4. Hence, or otherwise, determine :
(1) the minimum distance of the yacht from Ali; m
(2) the time when this occurs. ≈ seconds
