Question

在⊿ABC中，AD⊥AB,BC向量=√3BD向量，|AD|向量=1,则AC向量×AD向量= A.2√3 B. √3/2 C. √3/3 D. √3

解答过程要详细哦！

Answer 1

选D. √3
解：
因为BC=√3BD,
|AD|=1AC.AD
= (AD+DC). AD
= |AD|² + DC.AD
= 1 + (BC - BD). AD
= 1 + (√3BD - BD ).AD
= 1 + (√3-1)BD.AD
= 1 + (√3-1)|BD| |AD| cos ∠BDA
=1 + (√3-1 |AD|×(BD cos ∠BDA)
= 1 + (√3-1) |AD|²
= √3