Question

已知三角形ABC的外接圆半径为1,圆心为O,且3OA向量+4OB向量+5OC向量=0向量，则OC向

已知三角形ABC的外接圆半径为1,圆心为O,且3OA向量+4OB向量+5OC向量=0向量，则OC向量乘以AB向量的值为？

Answer 1

∵3

OA
+4

OB
+5

OC
=

0

∴3

OA
+4

OB
=-5

OC

∴9

OA
2+24

OA
•

OB
+16

OB
2=25

OC
2
∵A，B，C在圆上
∴OA=OB=OC=1
∴

OA
•

OB
=0
∴

OC
•

AB
=-
1
5
(3

OA
+4

OB
)• (

OB
-

OA
)
=-
1
5
(3

OA
•

OB
+4

OB
2-3

OA
2-4

OA
•

OB
)
=-
1
5

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