本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
The equations of the line / qkh4k6ziz.es. 5v k pcxkag7dhj:)6e $ L_{1}$ and $ L_{2}$ are
$\begin{array}{l}
L_{1}: \mathbf{r}_{1}=\left(\begin{array}{l}
2 \\
3 \\
1
\end{array}\right)+s\left(\begin{array}{c}
4 \\
-2 \\
4
\end{array}\right), s \in \mathbb{R} \\
L_{2}: \quad \mathbf{r}_{2}=\left(\begin{array}{l}
1 \\
3 \\
1
\end{array}\right)+t\left(\begin{array}{c}
-2 \\
1 \\
2
\end{array}\right), t \in \mathbb{R}
\end{array}$
1. Show that the lines $L_{1}$ and $ L_{2}$ are skew.
2. Find the acute angle between $ L_{1} $ and $L_{2} $, giving your answer correct to the nearest degree.
3. 1. Find a vector perpendicular to both lines.
2. Hence determine an equation of the line $ L_{3}$ that is perpendicular to both $ L_{1} $ and $ L_{2} $ and intersects both lines.
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