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![](https://rs.olm.vn/images/avt/0.png?1311)
Gt ⇒ \(2\left|\overrightarrow{MC}+\overrightarrow{MA}+\overrightarrow{MB}\right|=3\left|\overrightarrow{MB}+\overrightarrow{MC}\right|\)
Do G là trọng tâm của ΔABC
⇒ \(\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}=3\overrightarrow{MG}\)
⇒ VT = 6MG
I là trung điểm của BC
⇒ \(\overrightarrow{MA}+\overrightarrow{MB}=2\overrightarrow{MI}\)
⇒ VP = 6MI
Khi VT = VP thì MG = MI
Vậy tập hợp các điểm M thỏa mãn ycbt là đường trung trực của đoạn thẳng IG
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left|\overrightarrow{AB}-\overrightarrow{BC}\right|=\left|\overrightarrow{AB}+\overrightarrow{CB}\right|=BD=a\sqrt{6}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
** M là trung điểm của AB đúng không bạn?
a.
\(|\overrightarrow{AM}+\overrightarrow{AB}|=|\frac{1}{2}\overrightarrow{AB}+\overrightarrow{AB}|=\frac{3}{2}|\overrightarrow{AB}|=\frac{3}{2}.3a=\frac{9a}{2}\)
b.
\(|\overrightarrow{AB}+\overrightarrow{CD}|=|\overrightarrow{AB}+\overrightarrow{BA}|=|\overrightarrow{0}|=0\)
c.Trên $CD$ lấy $K$ sao cho $CK=a$. Khi đó:
\(|\overrightarrow{DN}+\overrightarrow{BN}|=|\overrightarrow{DN}+\overrightarrow{KD}|=|\overrightarrow{KN}|=KN=\sqrt{a^2+a^2}=\sqrt{2}a\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(BC=AD=\sqrt{AC^2-AB^2}=2a\)
a/ \(T=\left|3\overrightarrow{AB}-4\overrightarrow{BC}\right|\Rightarrow T^2=9AB^2+16BC^2-24\overrightarrow{AB}.\overrightarrow{BC}\)
\(=9a^2+64a^2=73a^2\Rightarrow T=a\sqrt{73}\)
b/ \(T^2=4AB^2+9BC^2+12.\overrightarrow{BA}.\overrightarrow{BC}=4AB^2+9BC^2=40a^2\)
\(\Rightarrow T=2a\sqrt{10}\)
c/ \(T=\left|\overrightarrow{AD}+3\overrightarrow{BC}\right|=\left|\overrightarrow{AD}+3\overrightarrow{AD}\right|=\left|4\overrightarrow{AD}\right|=4AD=8a\)
d/ \(T=\left|2\overrightarrow{DC}-3\overrightarrow{DC}\right|=\left|-\overrightarrow{DC}\right|=CD=AB=a\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\overrightarrow{AD}=\overrightarrow{BC}\Rightarrow T=\left|\overrightarrow{AB}+3\overrightarrow{AD}\right|\)
\(T^2=AB^2+9AD^2+6\overrightarrow{AB}.\overrightarrow{AD}\) (để ý rằng AB, AD vuông góc nên \(\overrightarrow{AB}.\overrightarrow{AD}=0\))
\(T^2=AB^2+9AD^2=2^2+9.3^2=85\)
\(\Rightarrow T=\sqrt{85}\)
Lời giải:
Trên tia đối tia $CB$ lấy $N$ sao cho $CB=CN$
\(|\overrightarrow{MC}+\overrightarrow{BC}|=|\overrightarrow{MC}+\overrightarrow{CN}|=|\overrightarrow{MN}|\)
Xét tam giác $BMC$ và $ADI$ có:
$\widehat{B}=\widehat{A}=90^0$
$\widehat{D}=\widehat{M}$ (cùng bù $\widehat{AMC})$
Do đó 2 tam giác này đồng dạng
$\Rightarrow \frac{BM}{BC}=\frac{AD}{AI}$
$\Rightarrow BM=BC.\frac{AD}{AI}=\frac{2BC^2}{AB}=\frac{3\sqrt{2}a}{4}$
$BN=2BC=a\sqrt{3}$
Do đó, áp dụng định lý Pitago:
$|\overrightarrow{MN}|=MN=\sqrt{BM^2+BN^2}=\frac{\sqrt{66}a}{4}$
Hình vẽ:
![](data:image/png;base64,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)