[填空题]
In this question, distance is in metres. Jack 7 cn8/1p1qqlxi q : 4rvheeokv50rl,nand John npv;s1 + ow) liz1 je0a (j+aetqaz2e6are flying airplanes in a straight line at a constant speed. Jack's aijvlw)ae s q1+j( ae+p1z06o; tnaie2zrplane passes through a point $\mathrm{P}$ . Its position, t seconds after it passes through $\mathrm{P}$ , is given by $\mathbf{r}_{1}=\left(\begin{array}{l}5 \\ 8 \\ 2\end{array}\right)+t\left(\begin{array}{c}-1 \\ 2 \\ 3\end{array}\right), t \in \mathbb{R} $.
1. (1) Write down the coordinates of P .(a,b,c) a= b= c =
(2) Find the speed of Jack's airplane in $\mathrm{ms}^{-1}$ .≈ $ms^{-1}$
2. After six seconds, Jack's airplane passes through a point Q .
(1) Find the coordinates of Q . (a,b,c) a= b= c =
(2) Find the distance the airplane has travelled during the six seconds.
John's airplane passes through a point R. Its position, s seconds after it passes through $R$ , is given by $\mathbf{r}_{2}=\left(\begin{array}{l}4 \\ 4 \\ 5\end{array}\right)+s\left(\begin{array}{c}-1 \\ 5 \\ 3\end{array}\right), s \in \mathbb{R}$ . ≈ m
3. Find the coordinates where the two airplanes intersect.(a,b,c) a= b= c =
4. Determine who is flying faster, Jack or John. Justify your answer.
