Question

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

Answer 1

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

Answer 2

how do you kow that ?

Answer 3

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

Answer 4

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.

Answer 5

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