问题 填空题
若平面上三点A、B、C满足|
AB
|=3,|
BC
|=4,|
CA
|=5,则
AB
BC
+
BC
CA
+
CA
AB
的值等于 ______.
答案

AB
+
BC
+
CA
=0可得(
AB
+
BC
+
CA
)2
=0,

∵|

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

|

AB
|2+|
BC
|
2
+|
CA
|
2
+2(
AB
BC
+
AB
AC
+
BC
AC
)=0,

9+16+25+2(

AB
BC
+
BC
CA
+
CA
AB
)=0

AB
BC
+
BC
CA
AB
=-25.

故答案为:-25

单项选择题
问答题 简答题