问题 选择题
若向量
a
b
c
满足
a
+
b
+
c
=
0
,且|
a
|=3,|
b
|=1,|
c
|=4,则
a
b
+
b
c
+
c
a
=(  )
A.-5B.5C.-13D.13
答案

a
+
b
+
c
=
0
,∴(
a
+
b
+
c
)2
=
a
2
+
b
2
+
c
2
+2
a
b
+2
b
c
+2
a
c
=
0
2
=0

2(

a
b
+
b
c
+
a
c
)=-(|
a
|2+|
b
|2+|
c
|2)
=-(32+12+42)=-26,

a
b
+
b
c
+
c
a
=-13.

故选:C.

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