问题 填空题
已知点A、B、C满足
|AB|
=3
|BC|
=4
|CA|
=5
,则
AB
BC
+
BC
CA
+
CA
AB
的值是______.
答案

|AB|
=3,
|BC|
=4,
|CA|
=5

|AB|
2+
|BC|
2
=
|CA|
2

AB
BC

AB
BC
+
BC
CA
+
CA
AB
=
BC
CA
+
CA
AB
=
CA
•(
AB
+
BC
)
=-
CA
2
=-25

故答案为-25

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