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=

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