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September 23rd, 2013, 10:41 AM   #1
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Proof - Two dimensional vectors

Hi all,

Could you please give me guidance on the following proof please?

Suppose we have three two-dimensional 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?

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September 23rd, 2013, 01:15 PM   #2
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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.
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September 23rd, 2013, 01:23 PM   #3
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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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