ACB is a straight line such that AC:CB=2:1.F diides ED in the ratio 1:r
(→OC)=(7/3)i + (4/3)j
(→OF)[(4+2r)/(1+r)]i+[(2+6r)/(1+r)]j
If O,C,F are collinear,find the value of r
http://i214.photobucket.com/albums/cc72/yesterday0721/11.jpg
amaths
2008-01-13 6:51 am
回答 (1)
2008-01-13 7:40 am
✔ 最佳答案
根據定義,若ai+bj//ci+dj,則a/c=b/d,其中i,j為單位向量(7/3)/[(4+2r)/(1+r)]=(4/3)/[(2+6r)/(1+r)]
[7(1+r)]/[3(4+2r)]=[4(1+r)/3(2+6r)]
(7+7r)(6+18r)=(4+4r)(12+6r)
42+168r+126r^2=48+72r+24r^2
102r^2+96r-6=0
17r^2+16r-1=0
(17r-1)(r+1)=0
r=1/17 or r=-1
收錄日期: 2021-04-25 17:20:01
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080112000051KK04761