Cho hai vec-tơ

B

- Hướng dẫn giải

Đáp án B

Cách 1:

Đặt  $\overrightarrow{AB}=\overrightarrow{a};\overrightarrow{AC}=\overrightarrow{b}\Rightarrow$$\left(\overrightarrow{AB},\overrightarrow{AC}\right)=\widehat{BAC}={120}^0$

Ta có $\left|\overrightarrow{AB}-\overrightarrow{AC}\right|=\left|\overrightarrow{BC}\right|=\left|\overrightarrow{a}-\overrightarrow{b}\right|$

Áp dụng định lý hàm cosin cho tam giác ABC ta có

 $B{C}^2=A{B}^2+A{C}^2$$-2AB.AC.\cos \widehat{BAC}=49$$\Rightarrow BC=7$

 Ta chọn B

Cách 2:

$\begin{array}{l}{\left(\overrightarrow{a}-\overrightarrow{b}\right)}^2={\overrightarrow{a}}^2+{\overrightarrow{b}}^2-2\overrightarrow{a}\overrightarrow{b}\\ ={\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2-2\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \left(\overrightarrow{a},\overrightarrow{b}\right)\\ =3^2+5^2-\mathrm{2.3.5.}\left(\frac{-1}{2}\right)=49\end{array}$

$\begin{array}{l}\Rightarrow {\left|\overrightarrow{a}-\overrightarrow{b}\right|}^2=49\\ \Rightarrow \left|\overrightarrow{a}-\overrightarrow{b}\right|=7\end{array}$

Ta chọn B