问题
选择题
已知P是边长为2的正△ABC的边BC上的动点，则
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答案
设
=AB a
=AC b
=t BP BC
则
=BC
-AC
=AB
-b
，a
2=4=a
2 b
•a
=2×2×cos60°=2b
=AP
+AB
=BP
+t﹙a
-b
﹚=﹙1-t﹚a
+t a b
+AB
=AC
+a b
•﹙AP
+AB
﹚=﹙﹙1-t﹚AC
+t a
﹚•﹙b
+a
﹚=﹙1-t﹚b
2+[﹙1-t﹚+t]a a
+t b
2b
=﹙1-t﹚×4+2+t×4=6
故选B．
