Question

角c等于90度,D是AB的中点,用向量法证明CD＝1/2AB

Answer 1

用[ ]表示向量

因为 AD=BD=AB/2

[AD]=[DB] ,[AB]=[AD]+[DB]=2[AD]

[CA]*[CB]=0

[CD]=[CA]+[AD]=[CB]+[BD]=[CB]-[AD]

[CD]^2=([CA]+[AD])*([CB]-[AD])

=[CA]*[CB]-[CA]*[AD]+[AD]*[CB]-[AD]^2

=0+[AD]*([CB]-[CA])-[AD]^2

=[AD]*([AB]-[AD])=[AD]^2

所以 CD=AD=AB/2