问题 填空题
已知三个向量
OA
OB
OC
两两之间的夹角为60°,又|
OA
|=1,|
OB
|=2
|
OC
|=3
,则|
OA
+
OB
+
OC
|
=______.
答案

由题意可得|

OA
+
OB
+
OC
|2=
OA
2
+
OB
2
+
OC
2

+2

OA
OB
+2
OA
OC
+2
OB
OC

=12+22+32+2(1×2×

1
2
+1×3×
1
2
+2×3×
1
2
)=25

|

OA
+
OB
+
OC
|=5

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