问题 解答题
已知
OA
=(2,1),
OB
=(t,-2),
OC
=(1,2t)

(1)若|
AB
|=5
,求t.
(2)若∠BOC=90°,求t.
(3)若A、B、C三点共线,求t.
答案

(1)|

AB
|=
(t-2)2+(-3)2
=5,t=6或-2.

(2)

OB
OC
=0,t-4t=0,t=0.

(3)∵

AB
=(t-2,-3),
AC
=(-1,2t-1)

A、B、C共线,

AC
=λ(
AB
)

(-3)×(-1)=(t-2)(2t-1),t=

33
4

单项选择题
单项选择题