Trong mặt phẳng $\displaystyle Oxy$ cho$A\left( 1;2 \right),\ B\left( 4;1 \right),\ C\left( 5;4 \right)$. Tính$\widehat{BAC}$ ? A. ${{60}^{\text{o}}}$ B. ${{45}^{\text{o}}}$ C. ${{90}^{\text{o}}}$ D. ${{120}^{\text{o}}}$
Đáp án đúng: B Chọn B Ta có $\overrightarrow{AB}=\left( 3;-1 \right)$,$\overrightarrow{AC}=\left( 4;2 \right)$ suy ra$\cos \left( \overrightarrow{AB};\overrightarrow{AC} \right)=\frac{\overrightarrow{AB}.\overrightarrow{AC}}{AB.AC}=\frac{10}{\sqrt{10}.\sqrt{20}}=\frac{\sqrt{2}}{2}$$\Rightarrow \left( \overrightarrow{AB};\overrightarrow{AC} \right)={{45}^{\text{o}}}$.