本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
Two lines L_{1} and L_{2} are rebmchp/ kl5nj8:* ;tyr p,fl 9 ooq1*sp2eha3qubn n8 x3resented by the vector equations:
$\begin{aligned}
L_{1}: & \mathbf{r}_{1}=\left(\begin{array}{l}
2 \\
1 \\
4
\end{array}\right)+t\left(\begin{array}{l}
0 \\
1 \\
2
\end{array}\right), t \in \mathbb{R} \\
L_{2}: & \mathbf{r}_{2}=\left(\begin{array}{c}
-1 \\
-3 \\
11
\end{array}\right)+s\left(\begin{array}{l}
1 \\
2 \\
k
\end{array}\right), s \in \mathbb{R}
\end{aligned}$
The lines $L_{1} $ and $ L_{2}$ are perpendicular to each other.
1. Show that k=-1 .
The lines L_{1} and L_{2} intersect at the point A .
2. Find $\overrightarrow{\mathrm{OA}}$ .
Let $ \overrightarrow{\mathrm{OB}}=\left(\begin{array}{l}2 \\ 2 \\ 7\end{array}\right)$ and $\overrightarrow{\mathrm{BC}}=\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$
3. 1. Find $\overrightarrow{\mathrm{BA}}$.
2. Hence find the angle CBA.
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