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已知向量=(1,1),向量与向量的夹角为,且=-1.(1)求向量;(2)若向量与=(1,0...
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已知向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAKZJREFU
OE/dU8ENwyAM9EjZJ1t4CJbwDh3Ac1hiBy9xNSRNoEFBlfqoiuCD786HbQi3KyOtCbnB0D0hojlh
WR8HjGJhfhakPc3nGb7/hjfFuaV/J5i8migwE5DYpep7lRzKAT4ABokJGOBRCVW5ixYBhvq1rQRX
MIWFNlbuWDHAg1wZ3Elt9vq7U416O5t3omLHEXvw6GqpqU6YO0kjwvQH9YAfHL4nsnDA6oII0T0A
AAAASUVORK5CYII=
)
=(1,1),向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALFJREFU
OE+tU20NxCAMRdL8zEVFYAIPJ6A6SPCAiXd0MMKNj26XkewX77MdBssTYHeL0GDMmpBug8W2fyrM
pAP922CLzXOH9ztcFPVIM4J3pbzzy5Q/DpEJCh4NIYLJYa2PhhAZpMmnsNUhx/Fw5yKJEQdtCkHi
SOkzUiaODDOhi5MFpoR+OuJA4EGm5NBPRwTMZADmGucA1y5966ND3bJM6Mmm1cfU7uEOWDD//613
Hb5HpsB0tmhR7AAAAABJRU5ErkJggg==
)
与向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAKZJREFU
OE/dU8ENwyAM9EjZJ1t4CJbwDh3Ac1hiBy9xNSRNoEFBlfqoiuCD786HbQi3KyOtCbnB0D0hojlh
WR8HjGJhfhakPc3nGb7/hjfFuaV/J5i8migwE5DYpep7lRzKAT4ABokJGOBRCVW5ixYBhvq1rQRX
MIWFNlbuWDHAg1wZ3Elt9vq7U416O5t3omLHEXvw6GqpqU6YO0kjwvQH9YAfHL4nsnDA6oII0T0A
AAAASUVORK5CYII=
)
的夹角为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAARFJREFU
SEvFlNsRxCAIRd2WbYdOqMMqbIIFTFbMS9HMrF+ZjB4ucOFDfMLKEcDKCSuPVb0CMlIMQVKhAMnF
ZEAiiEhZn/E3QzyMQDlvj0vgBF6AFZxgJoUaebIGRsJWzIilIiPn1MaMkcKvqH3E2QfOOhwAmTB6
uyARdxM5PVCd2E/19sZLs/CooNjbprl/S7u7ChIAT4jMG5DaQ7xi2iyr5JIu/1uXxwKQolvAWP2k
vUWJAsy4dlPQAGrxPRV2qg9QzLXLtlZPiMciXjjxOGBme4mQJgWlO91YAUwGTBOzUKpECLIXZ4ZJ
O7P1eArAfa1dmVAgW/jO5yMme2GhNGEmUmhlLgNGsm7vjA3TA/f/gC/QnNiGhmRq/gAAAABJRU5E
rkJggg==
)
,且
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAWCAYAAADXYyzPAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAARdJREFU
SEvtVe0NgyAQZST3cQuGYAl26ADMQeIOLPHKCRhBj8PWpG1Son8svM/TKnTXAjMbLP1Nwq/nGErE
XAym+SFu6+s/Yqi4IN8TTMe2fJ44aozPOf7ejt9rlz0tR/0LxN7mQbVelPuC4wCneYLgNAZ4cZ3Y
2+r1q0lIlIXsFzcTBwc9YjcWUTneOlJRNTljQLguU8wetnyUtENg2s7EubeNKB0eFJ+hS/cl6j7G
Srw6qFgIRMNxcs9cHGJOQjjxCnSAot2D0bNOTOe87TSTY168ol50ZS0prZ9Jr+VxmgmXmxFCU3XM
ZTBIaUC8xlYT80raptgg5ajLXyNFvicf493mpEzzwFRe/4CMa+nu/BPfFKQM8wTsfm7GU1x/hwAA
AABJRU5ErkJggg==
)
=-1.
(1)求向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALFJREFU
OE+tU20NxCAMRdL8zEVFYAIPJ6A6SPCAiXd0MMKNj26XkewX77MdBssTYHeL0GDMmpBug8W2fyrM
pAP922CLzXOH9ztcFPVIM4J3pbzzy5Q/DpEJCh4NIYLJYa2PhhAZpMmnsNUhx/Fw5yKJEQdtCkHi
SOkzUiaODDOhi5MFpoR+OuJA4EGm5NBPRwTMZADmGucA1y5966ND3bJM6Mmm1cfU7uEOWDD//613
Hb5HpsB0tmhR7AAAAABJRU5ErkJggg==
)
;
(2)若向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALFJREFU
OE+tU20NxCAMRdL8zEVFYAIPJ6A6SPCAiXd0MMKNj26XkewX77MdBssTYHeL0GDMmpBug8W2fyrM
pAP922CLzXOH9ztcFPVIM4J3pbzzy5Q/DpEJCh4NIYLJYa2PhhAZpMmnsNUhx/Fw5yKJEQdtCkHi
SOkzUiaODDOhi5MFpoR+OuJA4EGm5NBPRwTMZADmGucA1y5966ND3bJM6Mmm1cfU7uEOWDD//613
Hb5HpsB0tmhR7AAAAABJRU5ErkJggg==
)
与
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAALNJREFU
OE/dU9EJxSAMzEjdp1tkCJdwhw7gHII7uMS9pOYV65NI4X31oJSSu8slWoKLgrAHlI5DvkCqJWDb
j4tGAqyfDcHaPO/w/xkGx3WkdwsqErdD5FSRY3uPsC1lRCMqoSYWIWPChwia880tRxAnqfyCpPdQ
nBj0t1Xb9+5eHNWRDkcxnx6nmCW/fc/uGQkLbFf8ux2Hr0P30G1FtH5z3AW6AM9eZ7DwVyw9uAeR
ln84Pmm4t8Ip0tGWAAAAAElFTkSuQmCC
)
=(1,0)的夹角为
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAjCAYAAABGpiBAAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAM1JREFU
OE/FU9ENQyEIpCu7DpswB1O4BAVEq2jr3yvJS9R3gYM7XqIBtzDQLeAG8EqPg1gQwDrcvkLV2QAj
CuuhEoq/VZJSSNrvFoM4Y2kgRoEzqAqVltFB6KeUyUpAL1tOIMuipKNEJQXFmYmCk2cB6Z048ei0
V31+4neJzW5HSfr7f6wSenVuSdzGySY8BA1vZYEr8+KdWbvNT2NaX60yzZMRJFVLK7XwO9hXzf1x
Z1Jq9/hBSgdZRwsPJT/fdaVOAsdS5JX6ZZiH7fsG0udOohBexs8AAAAASUVORK5CYII=
)
,向量
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAWCAYAAAD0OH0aAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAKxJREFU
OE/dU9sNwyAMvJGyT7bwECzBDh2AOSKxA0tczatNwkuR+lVLSCD7HhgMTsPT7Ib+VIM5QLPecNtf
nzJocL02miLzXOH3d7gxri39KyA4SY8nLrDuAaEemyhdCnQiFMmgGAlojwEgOMqNcQqIycqcKaMi
2BGgWsp2Ln4PS4jTTO8O0c45GYth2brPYHy7Ur75gLlqobGzmChc7CzHTy2laeu1YwB+/L3fSqi8
ej/hqQ8AAAAASUVORK5CYII=
)
=(cosA,2cos
2![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAAjCAYAAACkejs5AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAPxJREFU
SEu1VIERwyAItCu7jpswB1O4BJFoE0Ew1ku9yzWX+vDAPx8qJ+wcBu6csAM6WQ5ATEz9ehKWG+Xb
+dudDpgJIgMS9Xcw8bdIkE1gA0Ug9T+no6SCXVQzRDNqzVGCguJZa2zZdBEPXStAphIo6iIegRko
bgFbxuBQRbAa9p1jm52kW2v3Sr/n2Cjfwx9n5wjgN/G9qNXFxPsZeyesvtu2+jvVxQTDtfkGMP1Z
Y0ggq+fSWHWNp2EBzIhiA5wGd7LO58jid1Q+BfKienaH7puod+y9k5G9KNekhppATHMvmpLjToq6
jC0+AOvW1o9Ned9W72l1MdI21QPLUNimep3ITAAAAABJRU5ErkJggg==
)
),其中A,C为△ABC的内角,且A+C=
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAjCAYAAACdHYpiAAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAASRJREFU
SEvFVdsRAyEIJC3bjp1Qh1XYBBHhfF0mQkwmztzHJbqyD7gHlQUniwFOFpwcrtVXgBSZhjwBKTtQ
gTJSiEmPJIoM0t73SJBTmm7MGFxV3DVgOp4K1iJTBHKcVxEvlEmPPf/uQt2bCUOkS07b8cvG6mQg
9PinN1QRWfmJdxHSqgOwaC1EV5jATuVLUbYq9mKfoQKNd6PXKYei+hYgRdEjYxSXOCtDw/EoeSGi
/DauZjNHfQSw0R9CtvTKloKEtJSt1tZuHUJiAODb+6AZ2z0hqoj1BtVijaD+x4r3amQvby0VFJua
KGKZNcbSjTlPE+lsHjin0TQPWlN56q8UxrUKZgjJzcZ/T2UJjUcGmD5rzgwsU9mg2GcD5T2woZl+
DPAEKRDaQOcyqmwAAAAASUVORK5CYII=
)
,求|
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAWCAYAAABOm/V6AAAAAXNSR0IArs4c6QAAAARnQU1BAACx
jwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAATNJREFU
SEvVld0NwyAMhBkp+2QLD8ES7NABmAMpO7CEiyEkDX8GykMbqQ9VnePznU0FNp8D5S7xaBcN/FrW
E6zCIXHbX2xZd0FBT7gH+c+GstMOXovOe+r9hhP/MRPdYc8X8nG0tI1CZeYPj29eEEadAzqiuhqC
qKyGsc7WQ1jUoJBz93KsuNr8+6Xw7pmwGmEkClJb7USIwqCKHYJGy81cBYK06NICbX3E4QIDdF+L
z+kERUGF0c4AwxpTdYL0AMFpEkicN1ERDBBZFAFqGoL0ks69Iy2IfCvIibp9XEqkFx0Ite2mnBP5
VrSoOYCglzTgYhONGRNpFGGQ5lbtivbzQAJg9PxMPHafHYS2F/c2nDdwx5Z9999R4Mmi4PPD5RDQ
0XnKtRzCX0yDkS6H6HA/K3kDhpt0NjCAXkgAAAAASUVORK5CYII=
)
|的最小值.
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