gjai gjup minh bai nay nha.thanks!

Question

cho A(2,1,-2),B(1,0,3),C(3,-1,1).tim D de ABCD la hinh thang can co day AB

score 2 · Answer 1

Gọi tọa độ D là (x,y,z)

$\overrightarrow{AB}$ (-1,-1,5)

$\overrightarrow{DC}$ (3-x, -1-y, 1-z)
ABCD là hình thang có AB//CD
=>

$\frac{3-x}{-1}=\frac{-1-y}{-1}= \frac{1-z}{5}=k$
=> Tọa độ của D

$\begin{cases}x= 3+k \\ y=-1+k\\z=1-5k \end{cases}$
=>

$\overrightarrow{AD}$ (1+k, k-2, 3-5k);

$\overrightarrow{BC}$ (2, -1, -2)
Có: AD=BC =>

$\sqrt{(1+k)^{2}+(k-2)^{2}+(3-5k)^{2}}= \sqrt{9}$
=> k= 5/27 hoặc k=1 (loại vì khi đó AD//BC)
Vậy tọa độ của D là: D(86/27, -22/27, 2/27)

chuẩn man! – babylionneu 07-01-13 08:54 PM

1 Đáp án