• 已知点A(2,1),B(0,2),C(-2,1),O(0,0).给出下面的结论:①OC∥BA;②OA⊥AB;③OA+OC=OB;④AC=OB-2OA.其中正确结论的个数是 个.试题及答案-填空题-云返教育

    • 试题详情

      已知点A(2,1),B(0,2),C(-2,1),O(0,0).给出下面的结论:
      OC
      BA

      OA
      AB

      OA
      +
      OC
      =
      OB

      AC
      =
      OB
      -2
      OA
      .其中正确结论的个数是          个.

      试题解答


      3
      解:由题意可得
      OC
      =(-2,1),
      BA
      =(2,-1),∴
      OC
      =-
      BA
      ,∴
      OC
      BA
      ,故①正确.
      OA
      =(2,1),
      AB
      =(-2,1),
      OA
      ?
      AB
      =-4+1=-3,故
      OA
      AB
      错误,即②不正确.
      OA
      +
      OC
      =(0,2),
      OB
      =(0,2),故
      OA
      +
      OC
      =
      OB
      ,即③正确.
      AC
      =
      OC
      -
      OA
      =(-4,0),
      OB
      -2
      OA
      =(0,2)-(4,2)=(-4,0),故④正确.
      故答案为 3.
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