anonymous 3 years ago Express the shortest vector as the sum or difference of two vectors

1. anonymous

|dw:1360027838692:dw|

2. anonymous

$\vec{u} - \vec{v} \textrm{ (aka \vec{w})}$

3. anonymous

how do you kow that ?

4. anonymous

like how do you know it's subtraction and not addition :S

5. anonymous

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.

6. anonymous

Thank you so much, you just made my life a lot easier !

7. anonymous

|dw:1360030795512:dw|

8. anonymous

AB+CB=AC ? would this be right

9. anonymous

That's definitely correct. If you are looking for the shortest vector however, I would find something that returns AB. If not, great job!

10. anonymous

AB= AC+CB