在三角形abc中 AD⊥AB,D在BC上 向量BC=√3向量BD 向量AD的膜=1 则向量AC*向量AD的值为

BC=√3BD,|AD|=1
AC.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|^2
= √3 #