Question

Suppose that u=<2,0>. describe the set of vectors v such that the magnitude of u+v=1

Answer 1

What's a vector that's length 1? Just a single vector that's rotating with radius 1, all these vectors are radius 1:

\[u+v = \langle \cos \theta, \sin \theta \rangle\]

Subtract u now since it's given, and you're done. It's a circle centered at a point!