Trong không gian Oxyz, cho đường thẳng $d:\left\{ \begin{aligned}...

Phương trình tham số đường thẳng \)">\Delta :\left\{ \begin{aligned}
& x=1+{t}' \\
& y=1-2{t}' \\
& z=1+2{t}' \\
\end{aligned} \right.B\left( 2;-1;3 \right)\in \Delta ,AB=3C\left( \dfrac{14}{5};\dfrac{17}{5};1 \right)C\left( -\dfrac{4}{5};-\dfrac{7}{5};1 \right)dAC=ABC\left( -\dfrac{4}{5};-\dfrac{7}{5};1 \right)\widehat{BAC}BCI\left( \dfrac{3}{5};-\dfrac{6}{5};2 \right)AI\overrightarrow{u}=\left( 2;11;-5 \right)\left\{ \begin{aligned}
& x=-1+2t \\
& y=-10+11t \\
& z=6-5t \\
\end{aligned} \right.d,{d}'\overrightarrow{{{u}_{d}}}.\overrightarrow{{{{{u}'}}_{{{d}'}}}}>0\overrightarrow{u}=\dfrac{\overrightarrow{{{u}_{d}}}}{\left| \overrightarrow{{{u}_{d}}} \right|}+\dfrac{\overrightarrow{{{u}_{{{d}'}}}}}{\left| \overrightarrow{{{u}_{{{d}'}}}} \right|}\overrightarrow{u}=\dfrac{\overrightarrow{{{u}_{d}}}}{\left| \overrightarrow{{{u}_{d}}} \right|}-\dfrac{\overrightarrow{{{u}_{{{d}'}}}}}{\left| \overrightarrow{{{u}_{{{d}'}}}} \right|}\overrightarrow{{{u}_{d}}}.\overrightarrow{{{{{u}'}}_{{{d}'}}}}<0\overrightarrow{u}=\dfrac{\overrightarrow{{{u}_{d}}}}{\left| \overrightarrow{{{u}_{d}}} \right|}-\dfrac{\overrightarrow{{{u}_{{{d}'}}}}}{\left| \overrightarrow{{{u}_{{{d}'}}}} \right|}\overrightarrow{u}=\dfrac{\overrightarrow{{{u}_{d}}}}{\left| \overrightarrow{{{u}_{d}}} \right|}+\dfrac{\overrightarrow{{{u}_{{{d}'}}}}}{\left| \overrightarrow{{{u}_{{{d}'}}}} \right|}$.