Question

Cho A(0,3),B(4,2). Điểm D thỏa vecto OD +2vecto DA -2 vecto DB=vecto 0, tọa độ D là

Answer 1

Gọi \(D\left(a;b\right)\) \(\Rightarrow\overrightarrow{OD}=\left(a;b\right)\) ; \(\overrightarrow{BA}=\left(-4;1\right)\)

\(\overrightarrow{OD}+2\left(\overrightarrow{DA}-\overrightarrow{DB}\right)=\overrightarrow{OD}+2\left(\overrightarrow{DA}+\overrightarrow{BD}\right)=\overrightarrow{OD}+2\overrightarrow{BA}\)

\(=\left(a-8;b+2\right)=\left(0;0\right)\)

\(\Rightarrow\left\{{}\begin{matrix}a-8=0\\b+2=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a=8\\b=-2\end{matrix}\right.\)