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a. Ta có:
$\begin{array}{l}\;{\overrightarrow u _{({d_1})}} = ( - 1;2;3);\;\;{\overrightarrow u _{({d_2})}} = (1;1;2);\,\,\;{M_1}(0;3; - 1) \in \left( {{d_1}} \right);\;{M_2}(4;0;3) \in \left( {{d_2}} \right)\\
\Rightarrow \;\overrightarrow {{M_1}{M_2}} \, = (4; - 3;4)\; \Rightarrow \left[ {{{\overrightarrow u }_{({d_1})}}.{{\overrightarrow u }_{({d_2})}}} \right].\overrightarrow {{M_1}{M_2}} = - 23 \ne 0
\end{array} $
$\Rightarrow \left( {{d_1}} \right)\,\,\,,\,\,\left( {{d_2}} \right)\,\,\,$ chéo nhau.
$ \begin{array}{l}{\rm{b}}{\rm{.}}\;\,\,{d_1} \cap (P) = A \Rightarrow A( - 2;7;5);\,{d_2} \cap (P) = B \Rightarrow B(3; - 1;1)\\
\Rightarrow \overrightarrow {AB} = (5; - 8; - 4)\\
\Rightarrow AB:\;\frac{{x + 2}}{5} = \frac{{y - 7}}{{ - 8}} = \frac{{z - 5}}{{ - 4}}
\end{array} $
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