D [ka+b=(k-1,k,2),2a-b=(3,2,-2),且(ka+b)·(2a-b)=3(k-1)+2k-4=0,解得k=.]
4.已知a=(1,2,-y),b=(x,1,2),且(a+2b)∥(2a-b),则( )
A.x=,y=1 B.x=,y=-4
C.x=2,y=- D.x=1,y=-1
B [a+2b=(2x+1,4,4-y),
2a-b=(2-x,3,-2y-2),
∵(a+2b)∥(2a-b),
∴∴]
5.已知a=(1-t,1-t,t),b=(2,t,t),则|a-b|的最小值为( )
A. B.
C. D.
C [∵a-b=(1-t,1-t,t)-(2,t,t)
=(-1-t,1-2t,0),
∴|a-b|==
=,∴|a-b|min=.]
二、填空题
6.已知a+b=(-1,-2,3),a-b=(1,0,1),则a=________,b=________.
(0,-1,2) (-1,-1,1) [a=
=(0,-1,2),