d nhận $
\hspace{0.33em}\hspace{0.33em}\overrightarrow{\mathbf{AB}}{\mathrm{(}}\mathrm{{-}}{6}{\mathrm{;}}{2}{\mathrm{)}}
$
làm VTCP
PTTS:
$
\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\left\{{\begin{array}{l}
{{x}\mathrm{{=}}{1}\mathrm{{-}}{6}{t}}\\
{{y}\mathrm{{=}}\mathrm{{-}}{2}\mathrm{{+}}{2}{t}}
\end{array}}\right.
$
Ta có:
$
\begin{array}{l}
{\hspace{0.33em}\overrightarrow{\mathbf{MA}}\mathrm{{=}}{3}\overrightarrow{\mathbf{OA}}\mathrm{{-}}{2}\overrightarrow{\mathbf{MB}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\overrightarrow{\mathbf{MA}}\mathrm{{=}}{\mathrm{(}}{1}\mathrm{{-}}{x}{\mathrm{;}}\mathrm{{-}}{2}\mathrm{{-}}{y}{\mathrm{)}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\overrightarrow{\mathbf{OA}}\mathrm{{=}}{\mathrm{(}}{1}{\mathrm{;}}\mathrm{{-}}{2}{\mathrm{)}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\overrightarrow{\mathbf{MB}}\mathrm{{=}}{\mathrm{(}}\mathrm{{-}}{5}\mathrm{{-}}{x}{\mathrm{;}}\mathrm{{-}}{y}{\mathrm{)}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Rightarrow}{1}\mathrm{{-}}{x}\mathrm{{=}}{3}{\mathrm{.}}{1}\mathrm{{-}}{2}{\mathrm{(}}\mathrm{{-}}{5}\mathrm{{-}}{x}{\mathrm{)}}\mathrm{\Rightarrow}{x}\mathrm{{=}}\mathrm{{-}}{4}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Rightarrow}\mathrm{{-}}{2}\mathrm{{-}}{y}\mathrm{{=}}\mathrm{{-}}{3}{\mathrm{.}}{3}\mathrm{{-}}{2}{\mathrm{.}}{y}\mathrm{\Rightarrow}{y}\mathrm{{=}}\mathrm{{-}}{7}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\longrightarrow}{M}{\mathrm{(}}\mathrm{{-}}{4}{\mathrm{;}}\mathrm{{-}}{7}{\mathrm{)}}}
\end{array}
$
PTTS:
$
\hspace{0.33em}\left\{{\begin{array}{l}
{{x}\mathrm{{=}}\mathrm{{-}}{4}\mathrm{{-}}{4}{t}}\\
{{y}\mathrm{{=}}\mathrm{{-}}{7}\mathrm{{+}}{2}{t}}
\end{array}}\right.
$
Mk bổ sung dưới này nha, Điểm M ko thay đổi nhé.
Ta có:$
\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\overrightarrow{\mathbf{AB}}{\mathrm{(}}\mathrm{{-}}{6}{\mathrm{;}}{2}{\mathrm{)}}
$
VTPT:$
\mathrm{\overrightarrow{n}}\mathrm{(}2\mathrm{;}6\mathrm{)}
$
PTTQ:
$
\begin{array}{l}
{{\mathrm{(}}{x}{\mathrm{;}}{y}{\mathrm{)}}\mathrm{\Longleftrightarrow}\overrightarrow{n}{vg}\overrightarrow{\mathbf{AN}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Longleftrightarrow}{2}{x}\mathrm{{-}}{7}{y}\mathrm{{+}}{\mathrm{[}}\mathrm{{-}}{2}{\mathrm{.(}}{1}{\mathrm{)}}\mathrm{{+}}{7}{\mathrm{(}}\mathrm{{-}}{4}{\mathrm{)]}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Longleftrightarrow}{2}{x}\mathrm{{-}}{7}{y}\mathrm{{-}}{\mathrm{30}}\mathrm{{=}}{0}}
\end{array}
$
PTTQ:
$
\begin{array}{l}
{\hspace{0.33em}{P}{\mathrm{(}}{x}{\mathrm{;}}{y}{\mathrm{)}}\mathrm{\Longleftrightarrow}\overrightarrow{b}{vg}\overrightarrow{\mathbf{MP}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Longleftrightarrow}\mathrm{{-}}{4}{x}\mathrm{{+}}{2}{y}\mathrm{{+}}{\mathrm{[}}{4}{\mathrm{.(}}\mathrm{{-}}{4}{\mathrm{)}}\mathrm{{-}}{2}{\mathrm{(}}\mathrm{{-}}{7}{\mathrm{)]}}}\\
{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\mathrm{\Longleftrightarrow}\mathrm{{-}}{4}{x}\mathrm{{+}}{2}{y}\mathrm{{-}}{2}\mathrm{{=}}{0}}
\end{array}
$
