问题 填空题
OA
=(t,1)(t∈Z)
OB
=(2,4)
,满足|
OA
|≤3
,则当△OAB是直角三角形时t的值为______.
答案

∵OB=2

5
>OA

∴1°当∠AOB=90°时,有2t+4=0,

解得t=-2,

2°当∠OBA=90°时,有

BA
=
OA
-
OB
=(t-2,-3)

OB
BA
=2(t-2)-12=0,

解得t=8,

因为|

OA
|≤3,所以t=8,不满足题意,舍去,

3°当∠OAB=90°,

OA
BA
=0,

t(t-2)-3=0,解得t=-1或t=3(舍去);

综上t=-2,或t=-1;

故答案为:-2或-1.

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