Definition of addition of vectors I know that a vector is an arrow defined by its magnitude and direction. The addition of two vectors is defined by the triangle law of addition. But why is it defined in this way? Is there a specific a reason to define addition of vectors in such a weird way.(Yes, it seems to me a little0 weird.)
 A: What you mention as a vector comes from more of a physics intuition. Vectors in that sense describe physical notions like forces, velocities and accelerations. If you're asking where the definitions of the 'triangle law' or parallelogram law come from, it's that they reflect the world we live in. It's pretty straightforward to realize that when two physical quantities (like velocity, acceleration etc.) act at one point, the result does not equal the sum of their magnitudes.
To picture this imagine paddling at 2km/h against a river flowing at 10km/h. The result isn't that you go at 12km/h, but rather you move backwards at 8km/h. This physical reality lead us to define vector addition (at least in this context) as respecting these triangle laws and parallelogram laws.
Like others have alluded to in the comments, once we generalize, vectors are no longer associated with the physical entity you're familiar with, but are abstract elements of some vector space which may have varying definitions of what vector addition ''looks like.''
