设O为坐标原点,已知向量OA=（1,2,3）,向量OB=（2,1,2）,向量OP=（1,1,2）,点Q在直线OP上运动,

OP = (1,1,2)
let
OQ = kOP =k(1,1,2) where k is a constant.
D= QA.QB
= (OQ-OA).(OQ-OB)
= (k-1,k-2,2k-3).(k-2,k-1,2k-2)
= (k-1)(k-2)+(k-2)(k-1) + (2k-3)(2k-2)
= 2k^2-6k+4 +4k^2-10k+6
= 6k^2-16k +10
D' = 12k-16 =0
k= 4/3
D'' = 12 >0 ( min )
Q的坐标 = (4/3)(1,1,2) = (4/3,4/3,8/3)