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