本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
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Jack and John are flying airplanes in a straight line at a constant speed.
Jack's airplane passes through a point P . Its position, t seconds after it passes through 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 .
2. Find the speed of Jack's airplane in $\mathrm{ms}^{-1} $.
2. After six seconds, Jack's airplane passes through a point Q .
1. Find the coordinates of Q .
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}$ .
3. Find the coordinates where the two airplanes intersect.
4. Is Jack or John flying faster? Justify your answer.
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