本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
The points $\mathrm{A}, \mathrm{B}$ and C have the following position vectors with respect to an origin O .
$\begin{array}{l}
\overrightarrow{\mathrm{OA}}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k} \\
\overrightarrow{\mathrm{OB}}=3 \mathbf{i}-2 \mathbf{j}+\mathbf{k} \\
\overrightarrow{\mathrm{OC}}=3 \mathbf{i}+2 \mathbf{j}-\mathbf{k}
\end{array}$
1. Find the vector equation of the line (A B) .
2. Determine whether the lines (AB) and (OC) are parallel, skew or intersecting.
3. Find the Cartesian equation of the plane $\Pi_{1}$ , that passes through the point A and is perpendicular to $ \overrightarrow{\mathrm{OC}}$.
4. Show that the line (A B) lies in the plane $\Pi_{1}$ .
The plane $ \Pi_{2} $ contains the points $\mathrm{O}, \mathrm{A}$ and C and the plane $\Pi_{3} $ contains the points $\mathrm{O}, \mathrm{B}$ and C .
5. Verify that $4 \mathbf{i}-5 \mathbf{j}+2 \mathbf{k}$ is perpendicular to the plane $ \Pi_{2} $.
6. Find a vector perpendicular to the plane $\Pi_{3}$ .
7. Find the acute angle between the planes $\Pi_{2} $ and $\Pi_{3}$ , giving your answer correct to the nearest degree.
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