Express the shortest vector as the sum or difference of two vectors

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Express the shortest vector as the sum or difference of two vectors

Mathematics
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|dw:1360027838692:dw|
\[\vec{u} - \vec{v} \textrm{ (aka $\vec{w}$)}\]
how do you kow that ?

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like how do you know it's subtraction and not addition :S
So when you add vectors, you put them tail to head and tail to head. An example of this in your picture is v and w summed together make u. When you subtract vectors, you put them starting from the same point and connect the heads. An example of this is v subtracted from u which makes w. Since there are only 3 vectors and you can combine only two of them, I brute forced all of the combinations, and based on your pictures, it seemed as through the solution I gave was best. However, with differently scaled vectors, one achieves different results.
Thank you so much, you just made my life a lot easier !
|dw:1360030795512:dw|
AB+CB=AC ? would this be right
That's definitely correct. If you are looking for the shortest vector however, I would find something that returns AB. If not, great job!
AB= AC+CB

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