本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
Consider the points dcckj-j ;m9n -w m*jr6 ;p/kj4be:o0ou+l22nv:szn r i )elwb$\mathrm{A}(3,2,-5) $ and $ \mathrm{B}(-3,6,-5)$ .
1. Find $\overrightarrow{\mathrm{AB}}$ .
Let C be a point such that $\overrightarrow{\mathrm{AC}}=\left(\begin{array}{l}3 \\ 0 \\ 2\end{array}\right)$ .
2. Find the coordinates of C .
The line L passes through B and is parallel to $\overrightarrow{\mathrm{AC}}$ .
3. Write down a vector equation of L in the form $\mathbf{r}=\mathbf{p}+t \mathbf{d}$ .
4. Given that $|\overrightarrow{\mathrm{AB}}|=k|\overrightarrow{\mathrm{AC}}|$ , find k .
The point D lies on L such that $|\overrightarrow{\mathrm{AB}}|=|\overrightarrow{\mathrm{BD}}| $.
5. Find the possible coordinates of D .
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