[填空题]
The displacement of a :i sn3b1 q1q mfon5qdw51a0hmremote-con(b0bfl qij-;z trolled toy yacht is modelled by the vector equationb z;q(f0bjli- $\mathbf{r}=\left(\begin{array}{c}
-5 \\
12
\end{array}\right)+t\left(\begin{array}{c}
1.5 \\
-2
\end{array}\right),$
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
