Mathematical and Physical Journal
for High Schools
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Problem A. 503. (March 2010)

A. 503. In space, there are given some vectors u1,u2,...,un and v such that |u1|\ge1, ..., |un|\ge1 and |v|\le1, and u1+...+un=0. Show that


(5 pont)

Deadline expired on April 12, 2010.


Lemma. If a,b are vectors such that |a|\ge1 and |b|\le1 then





To solve the problem, apply the lemma to a=ui, v=b and the apply the triangle inequality:



8 students sent a solution.
5 points:Backhausz Tibor, Bodor Bertalan, Éles András, Nagy 648 Donát, Szabó 928 Attila.
4 points:Nagy 235 János.
0 point:2 students.

Problems in Mathematics of KöMaL, March 2010