a/ Gọi \(M\left(0;y\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AM}=\left(1;y-1\right)\\\overrightarrow{BM}=\left(-2;y-2\right)\end{matrix}\right.\)
\(AM\perp BM\Rightarrow\overrightarrow{AM}.\overrightarrow{BM}=0\Rightarrow-2+\left(y-1\right)\left(y-2\right)=0\)
\(\Leftrightarrow y^2-3y=0\Rightarrow\left[{}\begin{matrix}y=0\\y=3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}M\left(0;0\right)\\M\left(0;3\right)\end{matrix}\right.\)
b/ Gọi \(N\left(x;0\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{NA}=\left(-1-x;1\right)\\\overrightarrow{NB}=\left(2-x;2\right)\end{matrix}\right.\)
\(\overrightarrow{NA}.\overrightarrow{NB}=\left|NA\right|.\left|NB\right|.cos60^0\)
\(\Leftrightarrow\left(-1-x\right)\left(2-x\right)+2=\frac{1}{2}\sqrt{\left(x+1\right)^2+1}\sqrt{\left(x-2\right)^2+4}\)
Nhìn pt ngán quá, hy vọng bạn tự giải được :D
