Trong mặt phẳng tọa độ Oxy, cho bốn điểm A(-8; 0), B(0; 4), C(2; 0), D(-3;-5

* Hướng dẫn giải

Đáp án D

Ta có:

$\overrightarrow{AB}=\left(8;4\right),\overrightarrow{AD}=\left(5;-5\right),\overrightarrow{CB}=\left(-2;4\right),\overrightarrow{CD}=\left(-5;-5\right)$

Suy ra $\left\{\begin{array}{c}\cos \left(\overrightarrow{AB},\overrightarrow{AD}\right)=\frac{8.5+4.(-5)}{\sqrt{8^2+4^2}\sqrt{5^2+5^2}}=\frac{1}{\sqrt{10}}\\ \cos \left(\overrightarrow{CB},\overrightarrow{CD}\right)=\frac{(-2).(-5)+4.(-5)}{\sqrt{2^2+4^2}\sqrt{5^2+5^2}}=-\frac{1}{\sqrt{10}}\end{array}\right.$

Suy ra

$$\begin{gathered} \cos \left(\overrightarrow{AB},\overrightarrow{AD}\right)+\cos \left(\overrightarrow{CB},\overrightarrow{CD}\right)=0 \\ \Rightarrow \widehat{BAD}+\widehat{BCD}={180}^0 \end{gathered}$$