題組內容

10. The following figure shows a square based pyramid with vetices at O(0, 0, 0), A(1, 0, 0), B(1, 1, 0), C(0, 1, 0) and D(0, 0, 1).5ed70936453e5.jpg

Π2 cuts AD and BD at the points P and Q respectively.(d) Show that P is the midpoint of AD. [2 分]

詳解 (共 1 筆)

詳解 提供者：浪漫名師na

由上題可知Π2: x+y-z=0，AD向量(-1,0,1)

Π2與AD切於P點

設AD上P點座標(1-t,0,t)

上式由A點座標(1,0,0)加上AD向量(-t,0,t)組合

也可由D點(0,0,1)加上AD向量(-t,0,t)組合，答案會一樣

P點座標(1-t,0,t)帶入Π2: x+y-z=0

得1-2t=0，得t=0.5

帶入(1-t,0,t)得P點為(0.5,0,0.5)為AD中點

故 P is the midpoint of AD