已知A(1,2)B(3,-2)C(9,7),若E,F为线段BC的三等份点,则AE向量×AF向量=
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![已知A(1,2)B(3,-2)C(9,7),若E,F为线段BC的三等份点,则AE向量×AF向量=](/uploads/image/z/5297699-11-9.jpg?t=%E5%B7%B2%E7%9F%A5A%281%2C2%29B%283%2C-2%29C%289%2C7%29%2C%E8%8B%A5E%2CF%E4%B8%BA%E7%BA%BF%E6%AE%B5BC%E7%9A%84%E4%B8%89%E7%AD%89%E4%BB%BD%E7%82%B9%2C%E5%88%99AE%E5%90%91%E9%87%8F%C3%97AF%E5%90%91%E9%87%8F%3D)
已知A(1,2)B(3,-2)C(9,7),若E,F为线段BC的三等份点,则AE向量×AF向量=
已知A(1,2)B(3,-2)C(9,7),若E,F为线段BC的三等份点,则AE向量×AF向量=
已知A(1,2)B(3,-2)C(9,7),若E,F为线段BC的三等份点,则AE向量×AF向量=
E,F为线段BC的三等份点
=> |BE|:|EC| = 1:2 and |BF|:|FC| = 2:1
=> OE = (2OB+OC)/3 and OF = (OB+2OC)/3
AE .AF
= (OE-OA).(OF-OA)
=( (2OB+OC)/3 - OA) .( (OB+2OC)/3 - OA)
= ( (5,1) - (1,2) ) .( (7,4) - (1,2))
= (4,-1).(6,2)
= 24-2 =22