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September 23rd, 2013, 10:41 AM  #1 
Newbie Joined: Sep 2013 Posts: 1 Thanks: 0  Proof  Two dimensional vectors
Hi all, Could you please give me guidance on the following proof please? Suppose we have three twodimensional vectors: a, b, and c. Given that the relation a+b+c=0 where 0 is the 0 vector. Could you prove that mod(c) <= mod(a) + mod(b) using a necessary and/or a sufficient condition? Thanks! 
September 23rd, 2013, 01:15 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,727 Thanks: 687  Re: Proof  Two dimensional vectors
I am not familiar with mod. Is this the same as length? In that case, the expressions is the triangle inequality. The condition that the sum is 0 means the vectors form a triangle.

September 23rd, 2013, 01:23 PM  #3 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: Proof  Two dimensional vectors
Applying the law of cosines, where is the angle between vectors and On the other hand . Since , we may conclude that . 

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