本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
A line $L_{1}$ passes through the points $\mathrm{A}(-2,0,1)$ and $\mathrm{B}(1,4,1) $.
1. Show that $ \overrightarrow{\mathrm{AB}}=\left(\begin{array}{l}3 \\ 4 \\ 0\end{array}\right) $
2. Hence write down:
1. a direction vector for $L_{1}$ ;
2. a vector equation for $L_{1}$ in the form $\mathbf{r}=\mathbf{a}+t \mathbf{b} $.
Another line $L_{2}$ is perpendicular to $ L_{1}$ and has vector equation
$\mathbf{r}=\left(\begin{array}{c}
4 \\
2 \\
-3
\end{array}\right)+s\left(\begin{array}{c}
k \\
-3 \\
1
\end{array}\right), s \in \mathbb{R}$
3. Find the value of k .
4. Show that the point $\mathrm{C}(-4,8,-5)$ lies on $ L_{2}$ .
5. Let D be the point such that A B C D is a parallelogram. Find $ \overrightarrow{\mathrm{OD}}$ .
参考答案: 
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