已知三点A(3,0,-1),B(1,2,3),C(4,1,2),求与平面ABC垂直的单位向量.

AB=(-2,2,4)AC=(1,1,3)BC=(3,-1,-1)令向量P垂直平面ABC,P=(x,y,z),则：P*AB=0P*AC=0P*BC=0即：-x+y+2z=0 x+y+3z=03x-y-z=0解得：x=-0。5z y=-2。5z令P为单位向量,则z^2=2/15代入求得x,y即可答案有两个,别漏解了!