Question

三角形ABC中,AC向量的绝对值=10,AD向量的绝对值=5,AD向量=5/11DB向量,CD向量*AB向量=0 （1）求（AB向量-AC

向量）的绝对值

Answer 1

|AC|=10, |AD|=5
AD = (5/11)DB,
CD.AB=0

AB = AD+DB
= AD + (11/5)AD
= (16/5)AD
|AB|^2 = (256/25). 25 = 256
|AB| = 16

AB.AC
= AB.(AD+DC)
=AB.(AD-CD)
=AB.AD -AB.CD
=|AB||AD| (AB//AD)
=16.5 =80

|AB-AC|^2
=(AB-AC).(AB-AC)
= |AB|^2 +|AC|^2 - 2AB.AC
= 256 + 100 - 2(80)
= 196
|AB-AC| = 14

Answer 2

14
AD向量=5/11DB向量 D在AB上 AD=5 BD=11
CD向量*AB向量=0 CD垂直于AB
(AB向量-AC向量)的绝对值=CB向量的绝对值
勾股定理 DC^2=75 CB=14