MathDB
Problems
Contests
International Contests
Tournament Of Towns
1992 Tournament Of Towns
(331) 3
(331) 3
Part of
1992 Tournament Of Towns
Problems
(1)
TOT 331 1992 Spring O S3 sum of vectors not zero
Source:
6/9/2024
Let
O
O
O
be the centre of a regular
n
n
n
-gon whose vertices are labelled
A
1
A_1
A
1
,
.
.
.
...
...
,
A
n
A_n
A
n
. Let
a
1
>
a
2
>
.
.
.
>
a
n
>
0
a_1>a_2>...>a_n>0
a
1
>
a
2
>
...
>
a
n
>
0
. Prove that the vector
a
1
O
A
1
→
+
a
2
O
A
2
→
+
.
.
.
+
a
n
O
A
n
→
a_1\overrightarrow{OA_1}+a_2\overrightarrow{OA_2}+...+a_n\overrightarrow{OA_n}
a
1
O
A
1
+
a
2
O
A
2
+
...
+
a
n
O
A
n
is not equal to the zero vector.(D. Fomin, Alexey Kirichenko)
vector
geometry
Vectors