已知xyz中A(x1,y1,z1),B(x2,y2,z2),AB上一点C,AC/CB=m,求C点坐标

题目

已知xyz中A(x1,y1,z1),B(x2,y2,z2),AB上一点C,AC/CB=m,求C点坐标

答案

如题可知C点在AB上,而AC/CB=m,设C（x,y,z）,那么(x-x1)/(x2-x)=(y-y1)/(y2-y)=(z-z1)/(z2-z)=m.解之得：x=(x1+mx2)/(1+m),y=(y1+my2)/(1+m),z=(z1+mz2)/(1+m).所以C[(x1+mx2)/(1+m),(y1+my2)/(1+m),(z1+mz2)/(1+m)]....