Question

Trong không gian Oxyz, cho tứ giác ABCD, có A(1;5;3), AB→=(1;2;−6), AD→(−2;−4;3), tọa độ điểm I∈BD thỏa mãn

Answer 1

thoa man DI/BD=2/3

Answer 2

\(B\left(2;7;-3\right)\) ; \(D\left(-1;1;6\right)\)

\(I\left(x;y;z\right)\Rightarrow\left\{{}\begin{matrix}\overrightarrow{DI}=\left(x+1;y-1;z-6\right)\\\overrightarrow{DB}=\left(-3;-6;9\right)\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x+1=\frac{2}{3}.\left(-3\right)\\y-1=\frac{2}{3}.\left(-6\right)\\z-6=\frac{2}{3}.9\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-3\\y=-3\\z=12\end{matrix}\right.\) \(\Rightarrow I\left(-3;-3;12\right)\)