Cái này là hóa hay là toán vậy bạn?

dạ hoá

\(\widehat{ABC}=120^0\Rightarrow\widehat{DAB}=180^0-120^0=60^0\)

\(\Rightarrow\Delta ABD\) đều

Gọi E là trung điểm AD \(\Rightarrow\overrightarrow{BE}=\dfrac{1}{2}\overrightarrow{BD}+\dfrac{1}{2}\overrightarrow{BA}\)

\(\Rightarrow\overrightarrow{BG}=\dfrac{2}{3}\overrightarrow{BE}=\dfrac{1}{3}\overrightarrow{BD}+\dfrac{1}{3}\overrightarrow{BA}\)

\(\Rightarrow\overrightarrow{BG}+\overrightarrow{AD}=\dfrac{1}{3}\overrightarrow{BD}+\dfrac{1}{3}\overrightarrow{BA}+\overrightarrow{AD}=\dfrac{1}{3}\left(\overrightarrow{BA}+\overrightarrow{AD}\right)+\dfrac{1}{3}\overrightarrow{BA}+\overrightarrow{AD}\)

\(=\dfrac{2}{3}\overrightarrow{BA}+\dfrac{4}{3}\overrightarrow{AD}=-\dfrac{2}{3}\overrightarrow{AB}+\dfrac{4}{3}\overrightarrow{AD}\)

Đặt \(\overrightarrow{u}=\overrightarrow{BG}+\overrightarrow{AD}\Rightarrow\left|\overrightarrow{u}\right|^2=\left(-\dfrac{2}{3}\overrightarrow{AB}+\dfrac{4}{3}\overrightarrow{AD}\right)=\dfrac{4}{9}AB^2+\dfrac{16}{9}AD^2-\dfrac{16}{9}\overrightarrow{AB}.\overrightarrow{AD}\)

\(=\dfrac{4}{9}.4a^2+\dfrac{16}{9}4a^2-\dfrac{16}{9}.2a.2a.cos60^0=\dfrac{16}{3}a^2\)

\(\Rightarrow\left|\overrightarrow{u}\right|=\dfrac{4a\sqrt{3}}{3}\)

a: \(\overrightarrow{CN}=\dfrac{1}{2}\overrightarrow{CA}+\dfrac{1}{2}\overrightarrow{CB}\)

\(=\dfrac{1}{2}\overrightarrow{CB}+\dfrac{1}{2}\overrightarrow{BA}+\dfrac{1}{2}\overrightarrow{CB}\)

\(=\dfrac{1}{2}\overrightarrow{u}-\overrightarrow{v}\)

Chọn B

Chọn A

\(C2:y=ax^2+bx+c\) \(\left(P\right)\) \(đi\) \(qua\)\(M\left(1;5\right)vàN\left(-2;8\right)\)

\(\Rightarrow\left\{{}\begin{matrix}a+b+2=5\\4a-2b+2=8\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=2\\b=1\end{matrix}\right.\) \(\Rightarrow S=3a+4b+c=3.2+4+2=12\)

\(C3a,\Rightarrow\left\{{}\begin{matrix}\overrightarrow{AB}\left(2;-4\right)\\\overrightarrow{AC}\left(2;-1\right)\end{matrix}\right.\)

\(b,D\left(xo;yo\right)\Rightarrow ABCD\) \(là\) \(hbh\Leftrightarrow\overrightarrow{AB}=\overrightarrow{DC}\Leftrightarrow\left\{{}\begin{matrix}3-xo=2\\1-yo=-4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}xo=1\\yo=5\end{matrix}\right.\) \(\Rightarrow D\left(1;5\right)\)